l₁-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems : a linear programming approach

This paper is concerned with the l₁-gain performance analysis and positive filter design for a positive discrete-time Markov jump linear system (MJLS) by using a linear programming (LP) approach. First, by constructing a linear stochastic Lyapunov function and introducing an ‘‘equivalent’’ deterministic positive discrete-time linear system, necessary and sufficient conditions in the form of LP are derived for stochastic stability and l₁-gain performance of the positive discrete-time MJLS. Then a sufficient conditionon the existence of the desired positive l₁-gain filter is provided. The desired positive l₁-gain filter can bedesigned by solving a standard LP problem. The pest’s structured population dynamic model is employed to illustrate the effectiveness of the proposed method.