The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first tr...The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.展开更多
This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.S...This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.展开更多
We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio time- dependent density functional theory. The dipole responses are investigated each as a function of chain length...We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio time- dependent density functional theory. The dipole responses are investigated each as a function of chain length. They converge into a single resonance in the longitudinal mode but split into two transverse modes. As the chain length increases, the longitudinal plasmon mode is redshifted in energy while the transverse modes shift in the opposite direction （blueshifts）. In addition, the energy gap between the two transverse modes reduces with chain length increasing. We find that there are unique characteristics, different from those of other metallic chains. These characteristics are crucial to atomic-scale engineering of single-molecule sensing, optical spectroscopy, and so on.展开更多
Chiroptical properties including electronic circular dichroism（ECD） and optical rotatory dispersion（ORD） of artemisinin and artemether have been fully studied using quantum-chemical calculation based on time-depen...Chiroptical properties including electronic circular dichroism（ECD） and optical rotatory dispersion（ORD） of artemisinin and artemether have been fully studied using quantum-chemical calculation based on time-dependent density functional theory.Both theoretical ECD and ORD of these two compounds were in good match with the experimental data.ECD spectrum of artemether could be totally attributed to the peroxide group,and that of artemisinin was an overlay of contribution from δ-lactone and peroxide moieties,which leading to a positive maximum at 260 nm.Our results showed that peroxide group could produce a broad ECD band in the far-UV region originated from electron transitions of HOMO →LUMO,HOMO-1 →LUMO and HOMO-2 →LUMO in the case of artemether.This work provided a theoretical interpretation of the ECD behavior of peroxide bond.展开更多
In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. W...In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. We study the convergence of the complex-valued system with impulsive control fields by one Lyapunov function based on the state distance and the invariant principle of impulsive systems. We propose new results for the mentioned complex-valued systems in the form of sufficient conditions and also present one numerical simulation to illustrate the effectiveness of the proposed control method.展开更多
Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of fi...Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.展开更多
By using first-principles simulations based on time-dependent density functional theory, the chemical reaction of an HCl molecule encapsulated in C60 induced by femtosecond laser pulses is observed. The H atom starts ...By using first-principles simulations based on time-dependent density functional theory, the chemical reaction of an HCl molecule encapsulated in C60 induced by femtosecond laser pulses is observed. The H atom starts to leave the Cl atom and is reflected by the C60 wall. The coherent nuclear dynamic behaviors of bond breakage and recombination of the HCl molecule occurring in both polarized parallel and perpendicular to the H-Cl bond axis are investigated. The radial oscillation is also found in the two polarization directions of the laser pulse. The relaxation time of the H-Cl bond lengths in transverse polarization is slow in comparison with that in longitudinal polarization. Those results are important for studying the dynamics of the chemical bond at an atomic level.展开更多
Time-dependent density functional theory(TDDFT)method is used to investigate the details of the excited state intramolecular proton transfer(ESIPT)process and the mechanism for temperature effect on the Enol^(*)/Keto^...Time-dependent density functional theory(TDDFT)method is used to investigate the details of the excited state intramolecular proton transfer(ESIPT)process and the mechanism for temperature effect on the Enol^(*)/Keto^(*)emission ratio for the Me_(2)N-substited flavonoid(MNF)compound.The geometric structures of the S_(0) and S_(1) states are denoted as the Enol,Enol^(*),and Keto*.In addition,the absorption and fluorescence peaks are also calculated.It is noted that the calculated large Stokes shift is in good agreement with the experimental result.Furthermore,our results confirm that the ESIPT process happens upon photoexcitation,which is distinctly monitored by the formation and disappearance of the characteristic peaks of infrared(IR)spectra involved in the proton transfer and in the potential energy curves.Besides,the calculations of highest occupied molecular orbital(HOMO)and lowest unoccupied molecular orbital(LUMO)reveal that the electronegativity change of proton acceptor due to the intramolecular charge redistribution in the S_(1) state induces the ESIPT.Moreover,the thermodynamic calculation for the MNF shows that the Enol^(*)/Keto^(*)emission ratio decreasing with temperature increasing arises from the barrier lowering of ESIPT.展开更多
Electronic properties, such as HOMO and LUMO energies, band gaps, ionization potential （IP） and electron affinity （EA） of 2,7- and 3,6-1inked carbazole trimers, two conjugated oligomcrs with different linkages of ...Electronic properties, such as HOMO and LUMO energies, band gaps, ionization potential （IP） and electron affinity （EA） of 2,7- and 3,6-1inked carbazole trimers, two conjugated oligomcrs with different linkages of carbazole, were studicd by the density functional theory with Becke-Lee-Young-Parr composite exchange correlation functional （B3LYP）. The absorption spectra of these compounds were also investigated by time-dependent density functional theory （TD-DFT） with 6-3 IG＊ basis set. The calculated results indicated that the HOMO and LUMO of the 2,7- and 3,6-1inked carbazole trimers are both slightly destabilized on going from methyl substitution to sec-butyl substitution. Both IP and EA exhibit their good hole-transporting but poor electronaccepting ability. The presence of alkyl groups on the nitrogen atoms does not affect the intra-chain electronic delocalization along the molecular frame. Thus no significant effect on the band gap and absorption spectra of compounds has been found.展开更多
The objective of this paper is to present a robust safety-critical control system based on the active disturbance rejection control approach, designed to guarantee safety even in the presence of model inaccuracies, un...The objective of this paper is to present a robust safety-critical control system based on the active disturbance rejection control approach, designed to guarantee safety even in the presence of model inaccuracies, unknown dynamics, and external disturbances. The proposed method combines control barrier functions and control Lyapunov functions with a nonlinear extended state observer to produce a robust and safe control strategy for dynamic systems subject to uncertainties and disturbances. This control strategy employs an optimization-based control, supported by the disturbance estimation from a nonlinear extended state observer. Using a quadratic programming algorithm, the controller computes an optimal, stable, and safe control action at each sampling instant. The effectiveness of the proposed approach is demonstrated through numerical simulations of a safety-critical interconnected adaptive cruise control system.展开更多
This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firs...This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time.展开更多
Disability is defined as a condition that makes it difficult for a person to perform certain vital activities.In recent years,the integration of the concepts of intelligence in solving various problems for disabled pe...Disability is defined as a condition that makes it difficult for a person to perform certain vital activities.In recent years,the integration of the concepts of intelligence in solving various problems for disabled persons has become more frequent.However,controlling an exoskeleton for rehabilitation presents challenges due to their nonlinear characteristics and external disturbances caused by the structure itself or the patient wearing the exoskeleton.To remedy these problems,this paper presents a novel adaptive control strategy for upper-limb rehabilitation exoskeletons,addressing the challenges of nonlinear dynamics and external disturbances.The proposed controller integrated a Radial Basis Function Neural Network(RBFNN)with a disturbance observer and employed a high-dimensional integral Lyapunov function to guarantee system stability and trajectory tracking performance.In the control system,the role of the RBFNN was to estimate uncertain signals in the dynamic model,while the disturbance observer tackled external disturbances during trajectory tracking.Artificially created scenarios for Human-Robot interactive experiments and periodically repeated reference trajectory experiments validated the controller’s performance,demonstrating efficient tracking.The proposed controller is found to achieve superior tracking accuracy with Root-Mean-Squared(RMS)errors of 0.022-0.026 rad for all joints,outperforming conventional Proportional-Integral-Derivative(PID)by 73%and Neural-Fuzzy Adaptive Control(NFAC)by 389.47%lower error.These results suggested that the RBFNN adaptive controller,coupled with disturbance compensation,could serve as an effective rehabilitation tool for upper-limb exoskeletons.These results demonstrate the superiority of the proposed method in enhancing rehabilitation accuracy and robustness,offering a promising solution for the control of upper-limb assistive devices.Based on the obtained results and due to their high robustness,the proposed control schemes can be extended to other motor disabilities,including lower limb exoskeletons.展开更多
An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local ...An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.展开更多
The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First...The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.展开更多
基金National Natural Science Foundation (K19972 0 11)
文摘The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.
基金Project supported by the National Natural Science Foundation of China (Grant No.62176140)。
文摘This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11074176 and 10976019)the Research Fund for the Doctoral Program of Higher Education of China (Grant No.20100181110080)
文摘We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio time- dependent density functional theory. The dipole responses are investigated each as a function of chain length. They converge into a single resonance in the longitudinal mode but split into two transverse modes. As the chain length increases, the longitudinal plasmon mode is redshifted in energy while the transverse modes shift in the opposite direction （blueshifts）. In addition, the energy gap between the two transverse modes reduces with chain length increasing. We find that there are unique characteristics, different from those of other metallic chains. These characteristics are crucial to atomic-scale engineering of single-molecule sensing, optical spectroscopy, and so on.
基金supported by the Fundamental Research Funds for the Central Institutes of China(No.2012ZD03)
文摘Chiroptical properties including electronic circular dichroism（ECD） and optical rotatory dispersion（ORD） of artemisinin and artemether have been fully studied using quantum-chemical calculation based on time-dependent density functional theory.Both theoretical ECD and ORD of these two compounds were in good match with the experimental data.ECD spectrum of artemether could be totally attributed to the peroxide group,and that of artemisinin was an overlay of contribution from δ-lactone and peroxide moieties,which leading to a positive maximum at 260 nm.Our results showed that peroxide group could produce a broad ECD band in the far-UV region originated from electron transitions of HOMO →LUMO,HOMO-1 →LUMO and HOMO-2 →LUMO in the case of artemether.This work provided a theoretical interpretation of the ECD behavior of peroxide bond.
文摘In this paper, we investigate one kind of complex-valued systems with an impulsive control field, where the complex-valued system is governed by the Schrödinger equation, which is used for quantum systems, etc. We study the convergence of the complex-valued system with impulsive control fields by one Lyapunov function based on the state distance and the invariant principle of impulsive systems. We propose new results for the mentioned complex-valued systems in the form of sufficient conditions and also present one numerical simulation to illustrate the effectiveness of the proposed control method.
文摘Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.
基金Project supported by the National Natural Science Foundation of China （Grant Nos. 11074176 and 10976019） and the Doctoral Program of Higher Education of China （Grant No. 20100181110080）.
文摘By using first-principles simulations based on time-dependent density functional theory, the chemical reaction of an HCl molecule encapsulated in C60 induced by femtosecond laser pulses is observed. The H atom starts to leave the Cl atom and is reflected by the C60 wall. The coherent nuclear dynamic behaviors of bond breakage and recombination of the HCl molecule occurring in both polarized parallel and perpendicular to the H-Cl bond axis are investigated. The radial oscillation is also found in the two polarization directions of the laser pulse. The relaxation time of the H-Cl bond lengths in transverse polarization is slow in comparison with that in longitudinal polarization. Those results are important for studying the dynamics of the chemical bond at an atomic level.
基金Project supported by the National Basic Research Program of China(Grant No.2013CB922204)the National Natural Science Foundation of China(Grant Nos.11574115 and 11704146)the Natural Science Foundation of Jilin Province,China(Grant No.20150101063JC)
文摘Time-dependent density functional theory(TDDFT)method is used to investigate the details of the excited state intramolecular proton transfer(ESIPT)process and the mechanism for temperature effect on the Enol^(*)/Keto^(*)emission ratio for the Me_(2)N-substited flavonoid(MNF)compound.The geometric structures of the S_(0) and S_(1) states are denoted as the Enol,Enol^(*),and Keto*.In addition,the absorption and fluorescence peaks are also calculated.It is noted that the calculated large Stokes shift is in good agreement with the experimental result.Furthermore,our results confirm that the ESIPT process happens upon photoexcitation,which is distinctly monitored by the formation and disappearance of the characteristic peaks of infrared(IR)spectra involved in the proton transfer and in the potential energy curves.Besides,the calculations of highest occupied molecular orbital(HOMO)and lowest unoccupied molecular orbital(LUMO)reveal that the electronegativity change of proton acceptor due to the intramolecular charge redistribution in the S_(1) state induces the ESIPT.Moreover,the thermodynamic calculation for the MNF shows that the Enol^(*)/Keto^(*)emission ratio decreasing with temperature increasing arises from the barrier lowering of ESIPT.
基金The project was supported by the Scientific Research Fund of Hunan Provincial Education Department (No. 05A002)the Prominent Mid-youth Science and Technology Foundation of Hunan Province (No. 04JJ1010)
文摘Electronic properties, such as HOMO and LUMO energies, band gaps, ionization potential （IP） and electron affinity （EA） of 2,7- and 3,6-1inked carbazole trimers, two conjugated oligomcrs with different linkages of carbazole, were studicd by the density functional theory with Becke-Lee-Young-Parr composite exchange correlation functional （B3LYP）. The absorption spectra of these compounds were also investigated by time-dependent density functional theory （TD-DFT） with 6-3 IG＊ basis set. The calculated results indicated that the HOMO and LUMO of the 2,7- and 3,6-1inked carbazole trimers are both slightly destabilized on going from methyl substitution to sec-butyl substitution. Both IP and EA exhibit their good hole-transporting but poor electronaccepting ability. The presence of alkyl groups on the nitrogen atoms does not affect the intra-chain electronic delocalization along the molecular frame. Thus no significant effect on the band gap and absorption spectra of compounds has been found.
基金supported by the Fondo para el Primer Proyecto of the Comitépara el Desarrollo de la Investigación(CODI)at the Universidad de Antioquia(Grant Number PRV2024-78509)。
文摘The objective of this paper is to present a robust safety-critical control system based on the active disturbance rejection control approach, designed to guarantee safety even in the presence of model inaccuracies, unknown dynamics, and external disturbances. The proposed method combines control barrier functions and control Lyapunov functions with a nonlinear extended state observer to produce a robust and safe control strategy for dynamic systems subject to uncertainties and disturbances. This control strategy employs an optimization-based control, supported by the disturbance estimation from a nonlinear extended state observer. Using a quadratic programming algorithm, the controller computes an optimal, stable, and safe control action at each sampling instant. The effectiveness of the proposed approach is demonstrated through numerical simulations of a safety-critical interconnected adaptive cruise control system.
基金co-supported by the National Natural Science Foundation of China(Nos.12372048,12102343)the Key Program of the National Natural Science Foundation of China(No.U2013206)+1 种基金the China Postdoctoral Science Foundation(No.2023M742835)the Guangdong Basic and Applied Basic Research Foundation,China(No.2023A1515011421).
文摘This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time.
基金funded by the King Salman Center For Disability Research,through Research Group No.KSRG-2024-468。
文摘Disability is defined as a condition that makes it difficult for a person to perform certain vital activities.In recent years,the integration of the concepts of intelligence in solving various problems for disabled persons has become more frequent.However,controlling an exoskeleton for rehabilitation presents challenges due to their nonlinear characteristics and external disturbances caused by the structure itself or the patient wearing the exoskeleton.To remedy these problems,this paper presents a novel adaptive control strategy for upper-limb rehabilitation exoskeletons,addressing the challenges of nonlinear dynamics and external disturbances.The proposed controller integrated a Radial Basis Function Neural Network(RBFNN)with a disturbance observer and employed a high-dimensional integral Lyapunov function to guarantee system stability and trajectory tracking performance.In the control system,the role of the RBFNN was to estimate uncertain signals in the dynamic model,while the disturbance observer tackled external disturbances during trajectory tracking.Artificially created scenarios for Human-Robot interactive experiments and periodically repeated reference trajectory experiments validated the controller’s performance,demonstrating efficient tracking.The proposed controller is found to achieve superior tracking accuracy with Root-Mean-Squared(RMS)errors of 0.022-0.026 rad for all joints,outperforming conventional Proportional-Integral-Derivative(PID)by 73%and Neural-Fuzzy Adaptive Control(NFAC)by 389.47%lower error.These results suggested that the RBFNN adaptive controller,coupled with disturbance compensation,could serve as an effective rehabilitation tool for upper-limb exoskeletons.These results demonstrate the superiority of the proposed method in enhancing rehabilitation accuracy and robustness,offering a promising solution for the control of upper-limb assistive devices.Based on the obtained results and due to their high robustness,the proposed control schemes can be extended to other motor disabilities,including lower limb exoskeletons.
基金Specialized Research Fund for the Doctoral Program of Higher Education ( No. 20090092110051)the Key Project of Chinese Ministry of Education ( No. 108060)the National Natural Science Foundation of China ( No. 51076027, 51036002, 51106024)
文摘An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.
基金The National Natural Science Foundation of China(No.60835001)the Key Project of Ministry of Education of China (No.108060)
文摘The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.
