Stochastic Nonlinear Systems With Random Input Switching State Stability

`Switched systems, as a typical kind of hybrid systems, have gained more and more efects inphysics, engineering, biology, information science and other real systems. For the inevitabil-ity of stochastic disturbance, much efort has been paid to the stochastic systems modelingproblems. As a class of important and complex systems, stochastic switched systems havegained a great deal of attention for its complexity and practicality. Considering that s-tochastic systems usually have a richer structure and can describe physical systems moreaccurately, many real process can be modeled as such systems. The input-to-state stabilitywhich shows efciency in characterizing the efects of external inputs on state property, hasdrawn much attention and some efcient results have been derived. However, less work refersto fnite-time stability and most of existing results are based on negative defnite Lyapunovfunction approach, which clearly is conservative in some sense. This paper mainly focuseson the input-to-state stability of stochastic switched nonlinear systems. The main resultsthat we derive are as follows:1) Finite-time stochastic input-to-state stability of stochastic impulsive switched non-linear systems.A group of stochastic impulsive switched nonlinear systems are studied to estimate thefnite-time stochastic input-to-state stability. Firstly, some conditions are given to checkthe stability in probability and fnite-time input-to-state stability for stochastic nonlinearsystems. Then, based on average dwell time technique, some sufcient results are used toestimate the fnite-time stochastic input-to-state stability for stochastic switched nonlinearsystems with or without impulses. Finally, a simulation demonstrates the efectiveness ofobtained results.2) Stochastic input-to-state stability of stochastic switched nonlinear systems based onan indefnite Lyapunov function.By means of the indefnite Lyapunov function method, stochastic nonlinear systemsis analyzed to ensure the stochastic input-to-state stability property. In terms of averagedwell time technique, the stochastic input-to-state stability of stochastic switched nonlinearsystems are estimated. At last, a numerical example illustrates the efciency of derivedresults.3) Stochastic integral input-to-state stability for stochastic impulsive switched nonlinearsystems with time delay. The stochastic integral input-to-state stability analysis is addressed for stochastic im-pulsive switched nonlinear systems with time delay. Based on Lyapunov-Krasovskii methodand average dwell-time technique, some sufcient criteria ensuring the stochastic integralinput-to-state property are obtained. Finally, a simulation example shows the efectivenessof derived results.