ℋ∞ filtering for discrete-time linear systems with Markovian jumping parameters

This paper investigates the problem of ℋ_∞ filtering for discrete-time linear systems with Markovian jumping parameters. It is assumed that the jumping parameter is available. We develop a methodology for designing discrete time Markovian jump linear filters which ensure a prescribed bound on the l₂-induced gain from the noise signals to the estimation error. Both the cases when the transition probability matrix for the Markov chain is exactly known and when it is uncertain but belongs to a fixed polytope are considered. The proposed design is based on the solution of linear matrix inequalities