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(infinity) 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(infinity)-gain performance, respectively. Furthermore, an l(infinity) 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(infinity)-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. (C) 2016 Elsevier Inc. All rights reserved.