Root mean square gain of discrete-time switched linear systems under dwell time constraints

被引:31
作者
Colaneri, P. [1 ]
Bolzern, P. [1 ]
Geromel, J. C. [2 ]
机构
[1] Politecn Milan, Dipartimento Elettron & Informaz, I-20133 Milan, Italy
[2] Univ Estadual Campinas, DSCE Sch Elect & Comp Engn, BR-13083852 Campinas, SP, Brazil
关键词
Switched linear systems; H-infinity control; Root mean square gain; Dwell time; LMI; LYAPUNOV FUNCTIONS; STABILITY; STABILIZATION; STABILIZABILITY;
D O I
10.1016/j.automatica.2011.02.035
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
This paper deals with discrete-time switched linear systems and considers the problem of computing an upper bound to the dwell time ensuring a pre-specified root mean square (RMS) gain. As a natural consequence of treating general systems of this class in terms of the order and the number of subsystems, only sufficient conditions are worked out. They depend on the complete separation of the stabilizing and anti-stabilizing solutions of the algebraic Riccati equation associated to each subsystem. Moreover, as positive features, it is shown that the dwell time preserving the specification can be calculated through linear matrix inequalities (LMIs) and line search, being thus numerically solvable in polynomial time, and this allows the treatment of stable switched linear systems which do not admit a common Lyapunov function. The case of a guaranteed RMS gain for arbitrary switching signals is also addressed. A simple academic example constituted by three subsystems of third order is included for illustration. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1677 / 1684
页数:8
相关论文
共 35 条
[1]  
Blanchini F, 2008, SYST CONTROL-FOUND A, P1
[2]   A survey of computational complexity results in systems and control [J].
Blondel, VD ;
Tsitsiklis, JN .
AUTOMATICA, 2000, 36 (09) :1249-1274
[3]   Transient and Asymptotic Analysis of Discrete-Time H∞-Filters [J].
Bolzern, P. ;
Colaneri, P. ;
De Nicolao, G. .
EUROPEAN JOURNAL OF CONTROL, 1997, 3 (04) :317-324
[4]   Multiple Lyapunov functions and other analysis tools for switched and hybrid systems [J].
Branicky, MS .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (04) :475-482
[5]  
Colaneri Patrizio, 2008, 16th Mediterranean Conference on Control & Automation, MED 2008, P107, DOI 10.1109/MED.2008.4602191
[6]   Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties [J].
Daafouz, J ;
Bernussou, J .
SYSTEMS & CONTROL LETTERS, 2001, 43 (05) :355-359
[7]   Perspectives and results on the stability and stabilizability of hybrid systems [J].
DeCarlo, RA ;
Branicky, MS ;
Pettersson, S ;
Lennartson, B .
PROCEEDINGS OF THE IEEE, 2000, 88 (07) :1069-1082
[8]   ON THE TIME-VARYING RICCATI DIFFERENCE EQUATION OF OPTIMAL FILTERING [J].
DENICOLAO, G .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1992, 30 (06) :1251-1269
[9]   Stability and stabilization of discrete time switched systems [J].
Geromel, JC ;
Colaneri, P .
INTERNATIONAL JOURNAL OF CONTROL, 2006, 79 (07) :719-728
[10]   Dynamic output feedback control of switched linear systems [J].
Geromel, Jose C. ;
Colaneri, Patrizio ;
Bolzern, Paolo .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (03) :720-733