Finite-time stochastic input-to-state stability of switched stochastic nonlinear systems

In this paper, the problems of finite-time globally asymptotical stability in probability (FGSP) and finite-time stochastic input-to-state stability (FSISS) for switched stochastic nonlinear (SSNL) systems are investigated. To solve these problems elegantly, some new definitions on FGSP and FSISS are presented in the form of generalized KLKL (GKLGKL) function, and some lemmas about GKLGKL functions and their properties are proved. Based on that, some sufficient conditions are provided firstly for nonswitched stochastic nonlinear (nSSNL) systems, which will make the corresponding study on SSNL systems easier. Then, overcoming the difficulties coming with the appearance of switching, some sufficient conditions on FGSP and FSISS are given for SSNL systems. Moreover, based on the concept of average dwell-time, a sufficient condition for FSISS of SSNL systems is also provided. Finally, some simulation examples are given to demonstrate the effectiveness of our results.