Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an ...Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an output feedback CNF controllaw are constructed respectively for the output regulation problemof singular linear systems with input saturation. It is shown thatthe output regulation problem by CNF control is solvable underthe same solvability conditions of the output regulation problemby linear control. However, with the virtue of the CNF control, thetransient performance of the closed-loop system can be improvedby carefully designing the linear part and the nonlinear part of theCNF control law. The design procedure and the improvement ofthe transient performance of the closed-loop system are illustratedwith a numerical simulation.展开更多
This paper deals with the problem of robust stability for continuous-time singular systems with state delay and parameter uncertainty. The uncertain singular systems with delay considered in this paper are assumed to ...This paper deals with the problem of robust stability for continuous-time singular systems with state delay and parameter uncertainty. The uncertain singular systems with delay considered in this paper are assumed to be regular and impulse free.By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed, which is derived by using Lyapunov-Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay-dependent result. The robust delay-dependent stability criterion proposed in this paper is a sufficient condition. Finally, numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.展开更多
Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind o...Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind of binary codebooks are constructed by using the subspace of the singular linear space over the finite fields.According to the anzahl theorem,the parameters and the maximum correlation amplitude I_(max)(C)of the codebooks are calculated,and then given the conditions that the I_(max)(C)asymptotically reaches the Welch bound.On this basis,by mixing with Hadamard matrices,the number of columns are increased and obtain another class of new code,which further relaxes the conditions that the I_(max)(C)asymptotically reaches the Welch bound.展开更多
In this paper, we propose DQMR algorithm for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax=b where is a singular and in general non-hermitian matrix that has an arb...In this paper, we propose DQMR algorithm for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax=b where is a singular and in general non-hermitian matrix that has an arbitrary index. DQMR algorithm for singular systems is analogous to QMR algorithm for non-singular systems. We compare this algorithm with DGMRES by numerical experiments.展开更多
The concept of finite-time stability for linear singular system is induced in this paper.Finite-time control problem is considered for linear singular systems with time-varying parametricuncertainties and exogenous di...The concept of finite-time stability for linear singular system is induced in this paper.Finite-time control problem is considered for linear singular systems with time-varying parametricuncertainties and exogenous disturbances. The disturbance satisfies a dynamical system with para-metric uncertainties. A su?cient condition is presented for robust finite-time stabilization via statefeedback. The condition is translated to a feasibility problem involving restricted linear matrix in-equalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities.Finally, an example is given to show the validity of the results.展开更多
This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based o...This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.展开更多
This paper deals with the problem of singular linear quadratic performance with the worst-disturbance rejection for descriptor systems. Under the conditions we give, the worst-disturbance and the optimal control-state...This paper deals with the problem of singular linear quadratic performance with the worst-disturbance rejection for descriptor systems. Under the conditions we give, the worst-disturbance and the optimal control-state pair are unique respectively, the optimal control can be synthesized as state feedback and the closed-loop system is regular, stable and impulse-free.展开更多
The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant ...The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and ＊-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.展开更多
The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for...The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
In this paper, we study the stability of discrete linear singular systems by switching controller. Using some recent results on multiple-Lyapunov function technique, we obtain two sufficient conditions of linear singu...In this paper, we study the stability of discrete linear singular systems by switching controller. Using some recent results on multiple-Lyapunov function technique, we obtain two sufficient conditions of linear singular systems.展开更多
This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzz...This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear singular system. The purpose of the robust stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties. In the robust H-infinity control problem, in addition to the stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequality (LMI) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.展开更多
This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict...This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.展开更多
For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smoot...For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.展开更多
Abstract In the paper,a concept of the essential numerical range W_(e)(T)of a linear relation T in a Hilbert space is given,other various essential numerical ranges W_(ei)(T),i=1,2,3,4,are introduced,and relationships...Abstract In the paper,a concept of the essential numerical range W_(e)(T)of a linear relation T in a Hilbert space is given,other various essential numerical ranges W_(ei)(T),i=1,2,3,4,are introduced,and relationships among W_(e)(T)and W_(ei)(T)are established.These results generalize relevant results obtained by Bogli et al.in[Bogli,S.,Marletta,M.and Tretter,C.,The essential numerical range for unbounded linear operators,J.Funct.Anal.,279,2020,47-12].Moreover,several fundamental properties of closed relations related to its operator parts are presented.In addition,singular discrete linear Hamiltonian systems including non-symmetric cases are considered,several properties for the associated minimal relations H_(0)are derived,and the above results for abstract linear relations are applied to H_(0).展开更多
The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is propo...The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.展开更多
The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singu...The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China(61374035)
文摘Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an output feedback CNF controllaw are constructed respectively for the output regulation problemof singular linear systems with input saturation. It is shown thatthe output regulation problem by CNF control is solvable underthe same solvability conditions of the output regulation problemby linear control. However, with the virtue of the CNF control, thetransient performance of the closed-loop system can be improvedby carefully designing the linear part and the nonlinear part of theCNF control law. The design procedure and the improvement ofthe transient performance of the closed-loop system are illustratedwith a numerical simulation.
文摘This paper deals with the problem of robust stability for continuous-time singular systems with state delay and parameter uncertainty. The uncertain singular systems with delay considered in this paper are assumed to be regular and impulse free.By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed, which is derived by using Lyapunov-Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay-dependent result. The robust delay-dependent stability criterion proposed in this paper is a sufficient condition. Finally, numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.
文摘Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind of binary codebooks are constructed by using the subspace of the singular linear space over the finite fields.According to the anzahl theorem,the parameters and the maximum correlation amplitude I_(max)(C)of the codebooks are calculated,and then given the conditions that the I_(max)(C)asymptotically reaches the Welch bound.On this basis,by mixing with Hadamard matrices,the number of columns are increased and obtain another class of new code,which further relaxes the conditions that the I_(max)(C)asymptotically reaches the Welch bound.
文摘In this paper, we propose DQMR algorithm for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax=b where is a singular and in general non-hermitian matrix that has an arbitrary index. DQMR algorithm for singular systems is analogous to QMR algorithm for non-singular systems. We compare this algorithm with DGMRES by numerical experiments.
文摘The concept of finite-time stability for linear singular system is induced in this paper.Finite-time control problem is considered for linear singular systems with time-varying parametricuncertainties and exogenous disturbances. The disturbance satisfies a dynamical system with para-metric uncertainties. A su?cient condition is presented for robust finite-time stabilization via statefeedback. The condition is translated to a feasibility problem involving restricted linear matrix in-equalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities.Finally, an example is given to show the validity of the results.
基金This work was supported by the National Natural Science Foundation of China (No. 6022130, 60334040, 60428304).
文摘This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.
基金This work was supported by Natural Science Foundation of Shandong Province (No. Y2004A05, Y2004A07)Science Technology Planning Project of Shandong Provincial Education Department(No. J05P51) and Science Research Foundation of Shandong Economic University
文摘This paper deals with the problem of singular linear quadratic performance with the worst-disturbance rejection for descriptor systems. Under the conditions we give, the worst-disturbance and the optimal control-state pair are unique respectively, the optimal control can be synthesized as state feedback and the closed-loop system is regular, stable and impulse-free.
基金supported by the National Natural Science Foundation of China (No.60774044)the Professional Research Foundation for Advanced Talents of Jiangsu University (No.07JDG037)+2 种基金the Natural Science Fund for Colleges and Universities in Jiangsu Province (No.08KJ510010)the Open Project of National Key Laboratory of Industrial Control Technology of Zhejiang University (No.ICT0910)Qing Lan Project of Jiangsu Province
文摘The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and ＊-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.
基金supported by Research Foundation of Education Bureau of Shannxi Province, PRC(No.2010JK400)
文摘The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
基金Supported by the Young Teacher from Henan Province(2004)
文摘In this paper, we study the stability of discrete linear singular systems by switching controller. Using some recent results on multiple-Lyapunov function technique, we obtain two sufficient conditions of linear singular systems.
基金National Natural Science Foundation of P. R. China (50477042)Ph. D. Programs Foundation of Ministry of Education of P.R.China (20040422052)the Natural Science Foundation of Shandong Province (Z2004G04)
基金supported by the National Natural Science Foundation of China (No.60574088, 60274014)the Research Plan Program of Scienceand Technology Ministry of Wuhan (No. 200950199019-07)
文摘This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear singular system. The purpose of the robust stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties. In the robust H-infinity control problem, in addition to the stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequality (LMI) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.
文摘This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.
基金Project supported by the National Science Foundation of China (10271097)
文摘For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.
基金supported by the National Natural Science Foundation of China(No.11971262)Shandong Province Natural Science Foundation(No.ZR2019MA038,ZR2024QA088)。
文摘Abstract In the paper,a concept of the essential numerical range W_(e)(T)of a linear relation T in a Hilbert space is given,other various essential numerical ranges W_(ei)(T),i=1,2,3,4,are introduced,and relationships among W_(e)(T)and W_(ei)(T)are established.These results generalize relevant results obtained by Bogli et al.in[Bogli,S.,Marletta,M.and Tretter,C.,The essential numerical range for unbounded linear operators,J.Funct.Anal.,279,2020,47-12].Moreover,several fundamental properties of closed relations related to its operator parts are presented.In addition,singular discrete linear Hamiltonian systems including non-symmetric cases are considered,several properties for the associated minimal relations H_(0)are derived,and the above results for abstract linear relations are applied to H_(0).
基金Supported by National Natural Science Foundation of China（60574011）
Acknowledgement The authors would like to thank Professor YANG Guang-Hong for his guidance.
基金supported by the National Natural Science Foundation of China(60774016).
文摘The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.
基金Supported by National High Technology Research and Development Program of China （863 Program） （2006AA04Z182）, National Natu- ral Science Foundation of China （60736021）, and National Creative Research Groups Science Foundation of China （60721062）
基金This work was supported by the National Creative Research Groups Science Foundation of China (No. 60421002) and the New Century 151 Talent Projectof Zhejiang Province.
文摘The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.
