Stochastic stability and [formula omitted]-gain analysis for positive nonlinear semi-Markov jump systems with time-varying delay via T-S fuzzy model approach

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This paper treats the issues of stochastic stability and L1-gain analysis for continuous-time positive fuzzy semi-Markov jump systems (PFSMJSs) with time-varying delay. The system under consideration involves semi-Markov stochastic process related to Weibull distribution. The practical systems such as Lotka–Volterra population model described by PFSMJSs always need to consider the sudden change in the operating process. To deal with these problems, a sufficient condition for stochastic stability of PFSMJSs is established, which is dependent of the bound of time-varying delay. Then, based on the obtained results, L1-gain performance is analyzed in standard linear programming (LP). Finally, Lotka–Volterra population model shows the validity of the conclusions.