Stability and L1-gain analysis of nonlinear positive Markov jump systems based on a switching transition probability. (February 2022) - Liu, Li-Juan; Xu, Ning; Zhao, Xudong
Abstract: This paper focuses on mean exponential stability and L 1 -gain analysis for nonlinear positive Markov jump systems (NPMJSs) based on a switching transition probability (STP), where sector nonlinear functions and delays are adopted. By developing a nonlinear stochastic copositive Lyapunov–Krasovskii functional (NSCLKF) approach, a sufficient condition for mean exponential stability of nonlinear positive time-delay Markov jump system is first presented under mode-dependent average dwell time (MDADT) switching by using linear programming (LP) approach. Further, L 1 -gain performance analysis is obtained. Moreover, the corresponding results for NPMJSs are given under average dwell time (ADT) switching. Illustrative results are provided to verify the validity of the theoretical results. Highlights: This paper studies stability for nonlinear positive Markov jump systems. MDADT approach is used against Markov process with STP and time-varying delays. NSCLKF approach is proposed by using LP technique. Minimum L 1 -gain value is obtained by solving optimization problem.