The Optimal Switched Law Methods Analysis and Research on Switched Linear Systems

The stable linear switched systems will converge to the balance Point. If different switched laws be chosen, the convergence Process will not be the same, so there is an optimal switched law. The issues of optimal switched law based on norm, convergence radius, convergence distance and convergence direction are respectively studied, and the optimal switched law is confirmed by solution of matrix equation. All kinds of instance have been considered synthetically, the synthetic optimal switched law is given, by which an optimal status of system in convergence process is reflected roundly. By calculate and simulation of practice examples and the using process of stability criterion is realized distinctly.

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Stability and controllability of switched systems

Bulletin of the Polish Academy of Sciences Technical Sciences ◽

10.2478/bpasts-2013-0055 ◽

2013 ◽

Vol 61 (3) ◽

pp. 547-555 ◽

Cited By ~ 32

Author(s):

J. Klamka ◽

A. Czornik ◽

M. Niezabitowski

Keyword(s):

Stability Analysis ◽

Asymptotic Stability ◽

Linear Systems ◽

Switched Systems ◽

Sufficient Conditions ◽

Switched Linear Systems ◽

Arbitrary Switching ◽

Mathematical Problems ◽

The Stability ◽

Necessary And Sufficient

Abstract The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

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A general stability criterion for switched linear systems having stable and unstable subsystems

International Journal of Adaptive Control and Signal Processing ◽

10.1002/acs.2373 ◽

2012 ◽

Vol 27 (11) ◽

pp. 1000-1011

Author(s):

Jesús San Martín ◽

Anthony G. O'Farrell

Keyword(s):

Linear Systems ◽

Stability Criterion ◽

Switched Linear Systems ◽

General Stability ◽

Unstable Subsystems

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Delay-Dependent Stability Criterion of Arbitrary Switched Linear Systems with Time-Varying Delay

Discrete Dynamics in Nature and Society ◽

10.1155/2010/347129 ◽

2010 ◽

Vol 2010 ◽

pp. 1-16 ◽

Cited By ~ 5

Author(s):

Jun Li ◽

Weigen Wu ◽

Jimin Yuan ◽

Qianrong Tan ◽

Xing Yin

Keyword(s):

Linear Systems ◽

Stability Criterion ◽

Linear Matrix ◽

Time Varying ◽

Switched Linear Systems ◽

Time Varying Delay ◽

Liner System ◽

Delay Dependent ◽

Delay Dependent Stability ◽

Varying Delay

This paper deals with the problem of delay-dependent stability criterion of arbitrary switched linear systems with time-varying delay. Based on switched quadratic Lyapunov functional approach and free-weighting matrix approach, some linear matrix inequality criterions are found to guarantee delay-dependent asymptotically stability of these systems. Simultaneously, arbitrary switched linear system can be expressed as a problem of uncertain liner system, so some delay-dependent stability criterions are obtained with the result of uncertain liner system. Two examples illustrate the exactness of the proposed criterions.

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Delay-Independent Stability of Switched Linear Systems with Unbounded Time-Varying Delays

Abstract and Applied Analysis ◽

10.1155/2012/560897 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11 ◽

Cited By ~ 16

Author(s):

Yuangong Sun

Keyword(s):

Stability Analysis ◽

Linear Systems ◽

Stability Criterion ◽

Switched System ◽

New Method ◽

Mixed Delays ◽

Time Varying ◽

Positive Systems ◽

Switched Linear Systems ◽

Arbitrary Switching

This paper is focused on delay-independent stability analysis for a class of switched linear systems with time-varying delays that can be unbounded. When the switched system is not necessarily positive, we first establish a delay-independent stability criterion under arbitrary switching signal by using a new method that is different from the methods to positive systems in the literature. We also apply this method to a class of time-varying switched linear systems with mixed delays.

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