Stochastic Stability of Discrete Time Positive Markov Jump Nonlinear Systems

This paper investigates the stochastic stability of discrete time positive Markov jump nonlinear systems (PMJNS). Some definitions on stochastic stability for discrete time PMJNS are introduced first. Then, using the multiply max-separable Lyapunov function method, some stochastic stability criterions of discrete time PMJNS are provided, and some corresponding criterions are also provided for discrete time positive Markov jump linear systems (PMJLS). Different from previous conclusions that require subsystems to be stable or marginally stable, the obtained results allow some subsystems to be unstable. Based on the proposed criterions, the stochastic stability behavior of discrete time positive Markov jump systems can be obtained just from the algebraic properties of the system function and the probability characteristics of the Markov chain. To illustrate the main results, two simulation examples are provided at the end.