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

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
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.

Stability and controllability of switched systems

2013 ◽  
Vol 61 (3) ◽  
pp. 547-555 ◽  
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.

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

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
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.

The Stabilization of Switched Time-Delay Linear Systems with Input Saturation

2014 ◽  
Vol 602-605 ◽  
pp. 2582-2585
Author(s):  
Li Jing ◽  
Li Liu
Keyword(s):  
Time Delay ◽  
Lyapunov Function ◽  
Linear Systems ◽  
Input Saturation ◽  
Switched System ◽  
New Method ◽  
System Stability ◽  
Sufficient Condition ◽  
Switched Linear Systems ◽  
System Controller

We focused on the stabilization of switched linear systems with time-delay and input saturation. First, the saturation part of each subsystem was dealt with by a new method and the system was transformed into a general switched system. Secondly, we proposed a sufficient condition for system stability based on Multi - Lyapunov Function. The sufficient condition is expressed into LMI and can be solved with MatLab. Further, we designed the system controller.

scholarly journals ℋ∞Performance and Stability Analysis of Linear Systems with Interval Time-Varying Delays and Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Stochastic Parameter ◽  
Stochastic Properties ◽  
Random Change

This paper deals with the problems ofℋ∞performance and stability analysis for linear systems with interval time-varying delays. It is assumed that the parameter uncertainties are of stochastic properties to represent random change of various environments. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative criteria of the concerned systems are introduced with the framework of linear matrix inequalities (LMIs). Four numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

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