An LP approach to full-order and reduced-order state estimations of positive Markov jump systems with delay

Abstract

ABSTRACTIn this paper, the problems of full-order and reduced-order positive state estimations are developed for discrete-time positive Markov jump linear systems with delay. By establishing a positive time-delay system for 1-moment function of the state vector, delay-dependent necessary and sufficient exponential stability conditions are first derived based on a comparison technique for positive systems. Then, on the basis of the derived stability conditions, the problems of designing positive state observers in full-order and reduced-order for positive Markov jump systems with delay are addressed. The existence conditions of positive observers and the design schemes are formulated in terms of linear programming problems which can be effectively solved by various optimisation algorithms to obtain the observer parameters. Finally, three numerical examples with simulations are given to validate the analysis and design results.