State estimation on positive Markovian jump systems with time-varying delay and uncertain transition probabilities

This paper is concerned with the state estimation problem based on an l ∞ observer for a class of positive discrete-time Markovian jump systems (MJSs). The system under consideration consists of time-varying delay and uncertain transition probabilities, where the transition probability matrix is described by a polytope set. Necessary and sufficient conditions are presented in linear programming (LP) form for the resulting error dynamic system to be stochastically stable and stochastically stable with an l ∞-gain performance, respectively. Furthermore, an l ∞ observer design scheme is presented to solve the state estimation problem such that the resulting error dynamic system is stochastically stable and achieves a prescribed l ∞-gain performance. All the proposed conditions are solvable in terms of LP with additional parameters. Finally, some examples are given to demonstrate the validity of the developed technique.