On the asymptotic stability of nonlinear nonstationary switching systems

2018 ◽  
pp. 20-32
Author(s):  
A. Platonov ◽  
Keyword(s):  
Asymptotic Stability ◽  
Switching Systems

scholarly journals Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching

2007 ◽  
Vol 49 (2) ◽  
pp. 231-241 ◽  
Author(s):  
Zhenting Hou ◽  
Hailing Dong ◽  
Peng Shi
Keyword(s):  
Markov Chain ◽  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Switching Systems ◽  
Switching System ◽  
Nonlinear Stochastic Systems ◽  
Semi Markov Process ◽  
Markovian Switching Systems ◽  
Semi Markov Processes

abstractIn this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system. Existing results for Markovian switching systems may then be applied to analyze phase semi-Markovian switching systems. In the following, we obtain asymptotic stability for the distribution of nonlinear stochastic systems with semi-Markovian switching. The results can also be extended to general semi-Markovian switching systems. Finally, an example is given to illustrate the feasibility and effectiveness of the theoretical results obtained.

Invariance principles

2012 ◽  
Author(s):  
Rafal Goebel ◽  
Ricardo G. Sanfelice ◽  
Andrew R. Teel
Keyword(s):  
Dynamical System ◽  
Asymptotic Stability ◽  
Dwell Time ◽  
Switching Systems ◽  
Output Function ◽  
Limit Sets ◽  
Time Switching ◽  
Invariance Principles ◽  
Invariance Properties ◽  
All Solutions

This chapter discusses invariance principles, which characterize the sets to which precompact solutions to a dynamical system must converge. They rely on invariance properties of ω‎-limit sets of solutions, and additionally on Lyapunov-like functions, which do not increase along solutions, or output functions. Invariance principles which rely on Lyapunov-like functions are first presented, and their applications to the analysis of asymptotic stability are then described. The chapter next states an invariance principle involving not a Lyapunov-like function, but an output function having a certain property not along all solutions, but only along the solution whose behavior is being analyzed. Finally, the chapter presents invariance principles for switching systems with dwell-time switching signals modeled as hybrid systems.

scholarly journals STABILITY OF ZERO SOLUTION OF SYSTEM WITH SWITCHES CONSISTING OF LINEAR SUBSYSTEMS

2020 ◽  
pp. 89-96
Author(s):  
D. Khusainov ◽  
A. Bychkov ◽  
A. Sirenko
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Switching Systems ◽  
Stability Of Solutions ◽  
Quadratic Lyapunov Function ◽  
Linear Differential ◽  
The Stability

In this paper, discusses the study of the stability of solutions of dynamic systems with switching. Sufficient conditions are obtained for the asymptotic stability of the zero solution of switching systems consisting of linear differential and difference subsystems. It is proved that the existence of a common quadratic Lyapunov function is sufficient for asymptotic stability.

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