CRITERION OF CHAOS FOR SWITCHED LINEAR SYSTEMS WITH CONTROLLERS

2010 ◽  
Vol 20 (12) ◽  
pp. 4103-4109 ◽  
Author(s):  
LINGLI XIE ◽  
YI ZHOU ◽  
YI ZHAO
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Dynamic Systems ◽  
Sufficient Criterion ◽  
Switched Linear Systems ◽  
Variable Parameters ◽  
Unstable Subsystem ◽  
Time Invariant

In this paper, a sufficient criterion for time-invariant switched linear systems with controllers to be chaotic in the sense of Li–Yorke and Devaney is presented. The switched linear systems consist of an unstable subsystem with expanding flows and a controllable subsystem. It is exposed that the controllability of dynamic systems, instead of asymptotic stability, plays an important role in generating chaos. Finally, we give a numerical simulation for an example with some variable parameters to illustrate the validity of the result.

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.

Asymptotic stability of linear systems with multiple time-invariant state-delays

2000 ◽  
Vol 33 (23) ◽  
pp. 91-96 ◽  
Author(s):  
Jianrong Zhang ◽  
Carl R. Knospe ◽  
Panagiotis Tsiotras
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Multiple Time ◽  
Invariant State ◽  
State Delays ◽  
Time Invariant

scholarly journals Global Stability of Polytopic Linear Time-Varying Dynamic Systems under Time-Varying Point Delays and Impulsive Controls

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
M. de la Sen
Keyword(s):  
Dynamic System ◽  
Linear Systems ◽  
Dynamic Systems ◽  
Linear Time ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Impulsive Controls ◽  
The Stability ◽  
Time Invariant ◽  
Point Delays

This paper investigates the stability properties of a class of dynamic linear systems possessing several linear time-invariant parameterizations (or configurations) which conform a linear time-varying polytopic dynamic system with a finite number of time-varying time-differentiable point delays. The parameterizations may be timevarying and with bounded discontinuities and they can be subject to mixed regular plus impulsive controls within a sequence of time instants of zero measure. The polytopic parameterization for the dynamics associated with each delay is specific, so that(q+1)polytopic parameterizations are considered for a system withqdelays being also subject to delay-free dynamics. The considered general dynamic system includes, as particular cases, a wide class of switched linear systems whose individual parameterizations are timeinvariant which are governed by a switching rule. However, the dynamic system under consideration is viewed as much more general since it is time-varying with timevarying delays and the bounded discontinuous changes of active parameterizations are generated by impulsive controls in the dynamics and, at the same time, there is not a prescribed set of candidate potential parameterizations.

Robust asymptotic stability of parametric switched linear systems with dwell time

2018 ◽  
Vol 12 (4) ◽  
pp. 477-483 ◽  
Author(s):  
Mohamad Ali Bagherzadeh ◽  
Javad Askari ◽  
Jafar Ghaisari ◽  
Mohsen Mojiri
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Dwell Time ◽  
Switched Linear Systems ◽  
Robust Asymptotic Stability

Simple sufficient conditions for asymptotic stability of positive linear systems for any switchings

2013 ◽  
Vol 61 (2) ◽  
pp. 343-347 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Discrete Time System ◽  
Time System ◽  
Switched Linear Systems ◽  
Time Linear

Abstract The asymptotic stability of positive switched linear systems for any switchings is addressed. Simple sufficient conditions for the asymptotic stability of positive switched continuous-time and discrete-time linear systems are established. It is shown that the positive switched continuous-time (discrete-time) system is asymptotically stable for any switchings if the sum of entries of every column of the matrices of subsystems is negative (less than 1)

Continuous-time Identification for a class of Switched Linear Systems

2020 ◽  
Author(s):  
Abdelhak Goudjil ◽  
Mathieu Pouliquen ◽  
Eric Pigeon ◽  
Olivier Gehan ◽  
Tristan Bonargent
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Switched Linear Systems
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