P-TH Moment And Almost Sure Stability Of Stochastic Switched Nonlinear Systems

Switched system is an indispensable class of hybrid dynamical systems, which is composed of a family of subsystems and a rule that orchestrates the switching among them. It has gained more and more effects in physics, biol-ogy, engineering, information science and any other fields. Yet, in the real sys-tems, for the inevitability of stochastic disturbance, much efforts have been paid to the stochastic systems modeling problems, so stochastic switched systems have become an important branch of system theory. Considering that stochastic switched systems usually have a richer structure and can describe many phe-nomenon more accurately.Moment and pathwise stability of stochastic switched nonlinear systems have investigated in this thesis. According to Lyapunov stability theorem, by introducing a class of ψ-type functions which have rich connotation and using the semi-martingale convergence theorem, improved exponential martingale in-equality and Razumikhin method, p-th moment ψγ stability and almost sure ψγ stability of stochastic switched nonlinear systems are obtained.Stability of stochastic switched nonlinear systems are investigated. Firstly, some sufficient conditions are given to check the p-th moment and almost sure ψγ stability of stochastic nonlinear systems. Then, based on the multiple Lya-punov functions approach, some sufficient conditions are derived to check the stability criteria of stochastic switched nonlinear systems. Finally, a simulation example shows the effectiveness of derived results.Stability of stochastic switched delay nonlinear systems and neutral stochas-tic switched nonlinear systems are investigated, respectively. Primarily, some sufficient conditions are given to check the p-th moment and almost sure ψγ stability of stochastic delay nonlinear systems and neutral stochastic nonlinear systems. Furthermore, based on Lyapunov-Razumikhin approach, some suffi-cient conditions are derived to check the stability criteria of stochastic switched nonlinear systems with delay and neutral stochastic switched nonlinear systems, respectively. In addition, the simulation example demonstrates the effectiveness of obtained results.