This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usua...This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.展开更多
This paper investigates the stability problem for sampled-data systems by adopting a refined semi-looped-functional,which is with the following two improvements.Firstly,the new functional term is with a new integral v...This paper investigates the stability problem for sampled-data systems by adopting a refined semi-looped-functional,which is with the following two improvements.Firstly,the new functional term is with a new integral vectorη0,which contains sampling information of the systems and associates two commonly used vectors.Secondly,the vectorη0 is combined into various zero equations for processing the functional,especially where a new equation is derived fromη0.Based on the refined functional,further stability results for sampled-data systems are obtained.And the effectiveness of the results is numerically verified through two examples at the end.展开更多
This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent,and not imposed to be definite positive.Based on the system inform...This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent,and not imposed to be definite positive.Based on the system information on the sampling interval wholly rather than partly,a new Lyapunovlike functional is constructed,which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state.To take advantage of the integral of the system state,integral equations of the sampled-data system are explored when estimating the derivative of the extended functional.By the Lyapunov-like functional theory,a new sampling dependent stability result is obtained for sampled-data systems without uncertainties.Then,the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived.At last,numerical examples are given to illustrate that the stability results improve over some existing ones.展开更多
This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data ...This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.展开更多
This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic s...This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic stability are considered. For networked discrete-time linear systems, the packet loss period is assumed to be a finite-state Markov chain. We establish that the mean-square stability of a related discrete-time system which evolves in random time implies the mean-square stability of the system in deterministic time by using the equivalence of stability properties of Markovian jump linear systems in random time. We also establish the equivalence of asymptotic stability for the systems in deterministic discrete time and in random time. For networked sampled-data systems, a binary Markov chain is used to characterize the packet loss phenomenon of the network. In this case, the packet loss period between two transmission instants is driven by an identically independently distributed sequence assuming any positive values. Two approaches, namely the Markov jump linear system approach and randomly sampled system approach, are introduced. Based on the stability results derived, we present methods for stabilization of networked sampled-data systems in terms of matrix inequalities. Numerical examples are given to illustrate the design methods of stabilizing controllers.展开更多
In this paper, we study a basic class of first order sampled-data control systems with unknown nonlinear structure and with sampling rate not necessarily fast enough, aiming at understanding the capability and limitat...In this paper, we study a basic class of first order sampled-data control systems with unknown nonlinear structure and with sampling rate not necessarily fast enough, aiming at understanding the capability and limitations of the sampled-data feedback. We show that if the unknown nonlinear function has a linear growth rate with its 'slope' (denoted by L) being a measure of the 'size' of uncertainty, then the sampling rate should not exceed 1/L multiplied by a constant (≈ 7.53) for the system to be globally stabilizable by the sampled-data feedback. If, however, the unknown nonlinear function has a growth rate faster than linear, and if the system is disturbed by noises modeled as the standard Brownian motion, then an example is given, showing that the corresponding sampled-data system is not stabilizable by the sampled-data feedback in general, no matter how fast the sampling rate is.展开更多
To control continuous-time uncertain dynamical systems with sampled data-feedback is prevalent today,but the sampling rate is usually not allowed to be arbitrarily fast due to various physical and/or computational con...To control continuous-time uncertain dynamical systems with sampled data-feedback is prevalent today,but the sampling rate is usually not allowed to be arbitrarily fast due to various physical and/or computational constrains.In this paper,the authors examine the limitations of sampled-data feedback control for a class of uncertain systems in continuous-time,with sampling rate not necessary fast enough and with the unknown system structure confined to a set of functions with both linear and nonlinear growth.The limitations of the sampled-data feedback control for the uncertain systems are established quantitatively,which extends the existing related results in the literature.展开更多
基金supported by the National Natural Science Foundation of China(61374090)the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Provincethe Taishan Scholarship Project of Shandong Province
文摘This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.62221004 and 62073166the Shandong Provincial Natural Science Foundation under Grant No.ZR2021ZD13+1 种基金the Postgraduate Research&Practice Innovation Program of Jiangsu Province under Grant No.KYCX230473the Project on the Technological Leading Talent Teams Led by Frontiers Science Center for Complex Equipment System Dynamics under Grant No.FSCCESD220401。
文摘This paper investigates the stability problem for sampled-data systems by adopting a refined semi-looped-functional,which is with the following two improvements.Firstly,the new functional term is with a new integral vectorη0,which contains sampling information of the systems and associates two commonly used vectors.Secondly,the vectorη0 is combined into various zero equations for processing the functional,especially where a new equation is derived fromη0.Based on the refined functional,further stability results for sampled-data systems are obtained.And the effectiveness of the results is numerically verified through two examples at the end.
基金the Natural Science Foundation of China under Grant No.61374090the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Provincethe Taishan Scholarship Project of Shandong Province。
文摘This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent,and not imposed to be definite positive.Based on the system information on the sampling interval wholly rather than partly,a new Lyapunovlike functional is constructed,which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state.To take advantage of the integral of the system state,integral equations of the sampled-data system are explored when estimating the derivative of the extended functional.By the Lyapunov-like functional theory,a new sampling dependent stability result is obtained for sampled-data systems without uncertainties.Then,the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived.At last,numerical examples are given to illustrate that the stability results improve over some existing ones.
基金This work was supported by the National Natural Science Foundation of China （Nos. 61104068, 61273119） Natural Science Foundation of Jiangsu Province （No. BK2010200）+1 种基金 China Postdoctoral Science Foundation Founded Project （No. 2012M511176） the Fundamental Research Funds for the Central Universities （No. 2242013R30006）.
文摘This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
基金Supported by Agency for Science, Technology and Research (Grant No. SERC 052 101 0037)the National Natural Science Foundation of China(Grant No. 60828006)NSFC-Guangdong Joint Foundation (Grant No. U0735003)
文摘This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic stability are considered. For networked discrete-time linear systems, the packet loss period is assumed to be a finite-state Markov chain. We establish that the mean-square stability of a related discrete-time system which evolves in random time implies the mean-square stability of the system in deterministic time by using the equivalence of stability properties of Markovian jump linear systems in random time. We also establish the equivalence of asymptotic stability for the systems in deterministic discrete time and in random time. For networked sampled-data systems, a binary Markov chain is used to characterize the packet loss phenomenon of the network. In this case, the packet loss period between two transmission instants is driven by an identically independently distributed sequence assuming any positive values. Two approaches, namely the Markov jump linear system approach and randomly sampled system approach, are introduced. Based on the stability results derived, we present methods for stabilization of networked sampled-data systems in terms of matrix inequalities. Numerical examples are given to illustrate the design methods of stabilizing controllers.
基金This work is supported by the National Natural Science Foundation of China and the National Key Project of China.
文摘In this paper, we study a basic class of first order sampled-data control systems with unknown nonlinear structure and with sampling rate not necessarily fast enough, aiming at understanding the capability and limitations of the sampled-data feedback. We show that if the unknown nonlinear function has a linear growth rate with its 'slope' (denoted by L) being a measure of the 'size' of uncertainty, then the sampling rate should not exceed 1/L multiplied by a constant (≈ 7.53) for the system to be globally stabilizable by the sampled-data feedback. If, however, the unknown nonlinear function has a growth rate faster than linear, and if the system is disturbed by noises modeled as the standard Brownian motion, then an example is given, showing that the corresponding sampled-data system is not stabilizable by the sampled-data feedback in general, no matter how fast the sampling rate is.
基金supported by National Natural Science Foundation of China under Grant No.11271339New Century Excellent Talents Program under Grant No.10-0141
文摘To control continuous-time uncertain dynamical systems with sampled data-feedback is prevalent today,but the sampling rate is usually not allowed to be arbitrarily fast due to various physical and/or computational constrains.In this paper,the authors examine the limitations of sampled-data feedback control for a class of uncertain systems in continuous-time,with sampling rate not necessary fast enough and with the unknown system structure confined to a set of functions with both linear and nonlinear growth.The limitations of the sampled-data feedback control for the uncertain systems are established quantitatively,which extends the existing related results in the literature.
