ANALYSIS and VERIFICATION of UNIFORM MOMENT EXPONENTIAL STABILITY for STOCHASTIC HYBRID SYSTEMS with POISSON JUMP

This paper is concerned with the analysis and verification of uniform moment exponential stability for a class of nonautonomous stochastic hybrid systems (SHSs), which contain not only continuous flows described by stochastic differential equations, but also Markovian switching and Poisson jump together. To start with, taking advantage of multiple Lyapunov functions (MLFs), we propose a necessary and sufficient condition for uniform pth moment exponential stability of nonlinear nonautonomous SHSs, in which indefinite scalar function is utilized to relax the conservativeness of the classical MLFs. Then, for linear nonautonomous SHSs, we further present a necessary and sufficient condition, described by verifiable time-varying linear matrix inequalities, for uniform mean square exponential stability by our less conservative MLFs and indefinite scalar function based method. Finally, we investigate the mechanical verification of the above two conditions for rational SHSs by proposing a semi-definite programming based computable approach. The applicabilities of both our theoretical results and mechanical approach are demonstrated by academic examples.