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 Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yuangong Sun ◽  
Zhaorong Wu ◽  
Fanwei Meng
Keyword(s):  
Stability Analysis ◽  
Complex Systems ◽  
Linear Systems ◽  
Algebraic Structure ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov functions play a key role in the stability analysis of complex systems. In this paper, we study the existence of a class of common weak linear copositive Lyapunov functions (CWCLFs) for positive switched linear systems (PSLSs) which generalize the conventional common linear copositive Lyapunov functions (CLCLFs) and can be used as handy tool to deal with the stability of PSLSs not covered by CLCLFs. We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained results.

scholarly journals New stability conditions for positive continuous-discrete 2D linear systems

2011 ◽  
Vol 21 (3) ◽  
pp. 521-524 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stability Conditions ◽  
Stability Tests ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

New stability conditions for positive continuous-discrete 2D linear systemsNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

scholarly journals Asymptotic stability of positive fractional 2D linear systems

2009 ◽  
Vol 57 (3) ◽  
pp. 289-292 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
2D Systems ◽  
The Stability ◽  
Necessary And Sufficient

Asymptotic stability of positive fractional 2D linear systemsNew necessary and sufficient conditions for the asymptotic stability of the positive fractional 2D systems are established. It is shown that the checking of the asymptotic stability of positive fractional 2D linear systems can be reduced to testing the stability of corresponding 1D positive linear systems.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

scholarly journals Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

2012 ◽  
Vol 22 (2) ◽  
pp. 401-408 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Andrzej Ruszewski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Type Model ◽  
Stability Tests ◽  
Numerical Examples ◽  
Computer Methods ◽  
Discrete Linear Systems ◽  
Complex Functions ◽  
The Stability

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systemsAsymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

Observability and Distinguishability Properties and Stability of Arbitrarily Fast Switched Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Najah F. Jasim
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
External Disturbances ◽  
Fast Switching ◽  
Nonlinear Switched Systems ◽  
Arbitrary Switching

This paper addresses sufficient conditions for asymptotic stability of classes of nonlinear switched systems with external disturbances and arbitrarily fast switching signals. It is shown that asymptotic stability of such systems can be guaranteed if each subsystem satisfies certain variants of observability or 0-distinguishability properties. In view of this result, further extensions of LaSalle stability theorem to nonlinear switched systems with arbitrary switching can be obtained based on these properties. Moreover, the main theorems of this paper provide useful tools for achieving asymptotic stability of dynamic systems undergoing Zeno switching.

Stability of positive fractional switched continuous-time linear systems

2013 ◽  
Vol 61 (2) ◽  
pp. 349-352
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Continuous Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Fractional Systems ◽  
Time Linear

Abstract The asymptotic stability of positive fractional switched continuous-time linear systems for any switching is addressed. Simple sufficient conditions for the asymptotic stability of the positive fractional systems are established. It is shown that the positive fractional switched systems are asymptotically stable for any switchings if the sum of entries of every column of the matrices of all subsystems is negative.

scholarly journals Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model

2016 ◽  
Vol 26 (4) ◽  
pp. 441-452 ◽  
Author(s):  
Andrzej Ruszewski
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
New Model ◽  
The Stability ◽  
Partition Method ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Linear Scalar

Abstract The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.

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