Finite-time boundedness and stabilization of switched linear systems

Haibo Du; Xiangze Lin; Shihua Li

Kybernetika (2010)

  • Volume: 46, Issue: 5, page 870-889
  • ISSN: 0023-5954

Abstract

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In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bounded and uniformly finite-time bounded are given. Moreover, to solve the finite-time stabilization problem, stabilizing controllers and a class of switching signals are designed. The main results are proven by using the multiple Lyapunov-like functions method, the single Lyapunov-like function method and the common Lyapunov-like function method, respectively. Finally, three examples are employed to verify the efficiency of the proposed methods.

How to cite

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Du, Haibo, Lin, Xiangze, and Li, Shihua. "Finite-time boundedness and stabilization of switched linear systems." Kybernetika 46.5 (2010): 870-889. <http://eudml.org/doc/196649>.

@article{Du2010,
abstract = {In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bounded and uniformly finite-time bounded are given. Moreover, to solve the finite-time stabilization problem, stabilizing controllers and a class of switching signals are designed. The main results are proven by using the multiple Lyapunov-like functions method, the single Lyapunov-like function method and the common Lyapunov-like function method, respectively. Finally, three examples are employed to verify the efficiency of the proposed methods.},
author = {Du, Haibo, Lin, Xiangze, Li, Shihua},
journal = {Kybernetika},
keywords = {switched linear systems; finite-time boundedness; multiple Lyapunov-like functions; single Lyapunov-like function; common Lyapunov-like function; switched linear systems; finite-time boundedness; multiple Lyapunov-like functions; single Lyapunov-like function; common Lyapunov-like function},
language = {eng},
number = {5},
pages = {870-889},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Finite-time boundedness and stabilization of switched linear systems},
url = {http://eudml.org/doc/196649},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Du, Haibo
AU - Lin, Xiangze
AU - Li, Shihua
TI - Finite-time boundedness and stabilization of switched linear systems
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 5
SP - 870
EP - 889
AB - In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bounded and uniformly finite-time bounded are given. Moreover, to solve the finite-time stabilization problem, stabilizing controllers and a class of switching signals are designed. The main results are proven by using the multiple Lyapunov-like functions method, the single Lyapunov-like function method and the common Lyapunov-like function method, respectively. Finally, three examples are employed to verify the efficiency of the proposed methods.
LA - eng
KW - switched linear systems; finite-time boundedness; multiple Lyapunov-like functions; single Lyapunov-like function; common Lyapunov-like function; switched linear systems; finite-time boundedness; multiple Lyapunov-like functions; single Lyapunov-like function; common Lyapunov-like function
UR - http://eudml.org/doc/196649
ER -

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