This paper focuses on the problem of observer design for a class of linear switched systems. By constructing appropriate Lyapunov functions and using matrix inequalities, conditions of the exponential convergence of the estimated state observer are obtained. Furthermore, by using state jump at certain time when the change of value of the switched law occurs and specifying the value of the state jump, the system performance is improved. It is shown that the convergence rate of the estimation error can be reduced significantly. Simulation results are given to show validity of the state observer.
YANG Yin, SUN Wen-an, PEI Bing-nan
. Observer Design for a Class of Linear Switched Systems[J]. Journal of Applied Sciences, 2014
, 32(1)
: 99
-104
.
DOI: 10.3969/j.issn.0255-8297.2014.01.016
[1]. XIE G, WANG L. Stabilization of switched linear systems with time-delay in detection of switching signal [J]. Journal of Mathematical Analysis and Applications, 2005, 305(1): 277-290.
[2] PETTERSSON S. Switched state jump observers for switched systems [C]//Proceedings of the 16th IFAC Word Congress, 2005, Prague. Tu–E12–TO/5.
[3] ZHANG Lixian, GAO Huijun. Asynchronously switched control of switched linear systems with average dwell time [J]. Automatica, 2010, 46(5): 953-958.
[4] LIU Jinfeng, MUÑOZ DE LA PEÑAB D, CHRISTOFIDES P D. Distributed model predictive control of nonlinear systems subject to asynchronousnext term and delayed measurements [J]. Automatica, 2010, 46(1): 52-61.
[5] PETTERSSON S. Observer design for switched systems using multiple quadratic Lyapunov functions [C]// 2nd IFAC Conference: Analysis and Design of Hybrid Systems, 2006, Alghero: 18-23.
[6] DE SANTIS E, DI BENEDETTO M D. Observer design for discrete-time linear switching systems [C]// Proceedings IFAC Workshop on Dependable Control of Discrete Systems, 2007, ENS Cachan, France: 311-316.
[7] XIE D, WANG Q, WU Y. Average dwell-time approach to L2 gain control synthesis of switched linear systems with time delay in detection of switching signal [J]. Control Theory & Applications, 2009, 3(6): 763-771.
[8] ZHANG Lixian, CUI Naigang, LIU Ming, ZHAO Ye. Asynchronous filtering of discrete-time switched linear systems with average dwell time [J]. IEEE Transactions on Circuits and Systems, 2011, 58(5): 1109-1118.
[9] 向峥嵘，向伟铭. 一类非线性切换系统观测器设计的新方法 [J]. 系统工程与电子技术，2009, 31(2): 416-419.
XIANG Zhengrong, XIANG Weiming. A new approach to observer design for a class of switched nonlinear systems [J]. Systems Engineering and Electronics, 2009, 31(2): 416-419. (in Chinese)
[10] KALMAN R E. A new approach to linear filtering and prediction problems [J]. ASME Journal of Basic Engineering, 1960, 82(4): 35-45.
[11] 顾则全，刘贺平，廖福成，王允建. 基于LMI的不确定时滞切换广义系统的保成本控制 [J], 系统工程与电子技术，2010, 32(1): 147-151.
GU Zequan, LIU Heping, LIAO Fucheng, WANG Yunjian. Guaranteed cost control for uncertain time-delay switched singular systems based on LMI [J]. Systems Engineering and Electronics, 2010, 32(1): 147-151. (in Chinese)
