Asymptotic Stability in Distribution of nonlinear Stochastic Systems with Semi-Markovian Switching

2008 ◽  
Vol 49 ◽  
Author(s):  
Hou Zhenting ◽  
Dong Hailing ◽  
Shi Peng
Keyword(s):  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Nonlinear Stochastic Systems ◽  
Stability In Distribution

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.

scholarly journals pth Mean Practical Stability for Large-Scale Itô Stochastic Systems with Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Yun ◽  
Huisheng Shu ◽  
Yan Che
Keyword(s):  
Comparison Principle ◽  
Large Scale ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Practical Stability ◽  
Nonlinear Stochastic Systems ◽  
Deterministic Systems ◽  
The One

Motivated by the study of a class of large-scale stochastic systems with Markovian switching, this correspondence paper is concerned with the practical stability in thepth mean. By investigating Lyapunov-like functions and the basic comparison principle, some criteria are derived for various types of practical stability in thepth mean of nonlinear stochastic systems. The main contribution of these results is to convert the problem of practical stability in thepth mean of stochastic systems into the one of practical stability of the comparative deterministic systems.

scholarly journals Asymptotic Stability of Delay-Controlled Nonlinear Stochastic Systems with Actuator Failures

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
N. Zhou ◽  
R. H. Huan
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Original System ◽  
Stochastic Averaging ◽  
Largest Lyapunov Exponent ◽  
Control Force ◽  
Nonlinear Stochastic Systems ◽  
Actuator Failures

The problem of asymptotic stability of delay-controlled nonlinear stochastic systems with actuator failures is investigated in this paper. Such a system is formulated as a continuous-discrete hybrid system based on the random switch model of failure-prone actuator. Time delay control force is converted into delay-free one by randomly periodic characteristic of the system. Using limit theorem and stochastic averaging, an approximate formula for the largest Lyapunov exponent of the original system is then derived, from which necessary and sufficient conditions for asymptotic stability are obtained. The validity and utility of the proposed procedure are demonstrated by using a stochastically driven nonlinear two-degree system with time delay feedback and actuator failure.

Sign in / Sign up

Export Citation Format

Share Document