BIBO stability of switched linear systems via arbitrary switching

2017 ◽  
Author(s):  
Cancan Chen ◽  
Zhendong Sun
Keyword(s):  
Linear Systems ◽  
Switched Linear Systems ◽  
Bibo Stability ◽  
Arbitrary Switching

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 Stabilization of Discrete-Time Planar Switched Linear Systems with Impulse

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yanli Zhu ◽  
Yuangong Sun
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
State Transition ◽  
Impulsive System ◽  
Switching Frequency ◽  
Sufficient Condition ◽  
Stabilization Problem ◽  
Switched Linear Systems ◽  
Switching Signal ◽  
Arbitrary Switching

We study the stabilization problem of discrete-time planar switched linear systems with impulse. When all subsystems are controllable, based on an explicit estimation on the state transition matrix, we establish a sufficient condition such that the switched impulsive system is stabilizable under arbitrary switching signal with given switching frequency. When there exists at least one uncontrollable subsystem, a sufficient condition is also given to guarantee the stabilization of the switched impulsive system under appropriate switching signal.

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.

Robust Control of Switched Linear Systems via Min of Quadratics

2013 ◽  
Author(s):  
Chengzhi Yuan ◽  
Fen Wu
Keyword(s):  
Lyapunov Function ◽  
Linear Systems ◽  
Output Feedback Control ◽  
Control Design ◽  
Quadratic Functions ◽  
Linear Matrix ◽  
Switched Linear Systems ◽  
Synthesis Conditions ◽  
Arbitrary Switching ◽  
Special Cases

In this paper, we will investigate the robust switching control problem for switched linear systems by using a class of composite quadratic functions, the min (of quadratics) function, to improve performance and enhance control design flexibility. The robustness is reflected in two prospectives including the ℋ ∞ performance and arbitrary switching of subsystems. A hysteresis min-switching strategy is employed to orchestrate the switching among a collection of controllers. The synthesis conditions for both state feedback and output feedback control problems are derived in terms of a set of linear matrix inequalities (LMIs) with linear search over scalar variables. The proposed min function based approach unifies the existing single Lyapunov function based method and multiple Lyapunov function based method in a general framework, and the derived LMI conditions cover the existing LMI conditions as special cases. Numerical studies are included to demonstrate the advantages of the proposed control design approach.

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