H∞ filtering for discrete-time Markovian jump systems with mode-dependent singularly perturbation parameters and partly unknown transition probabilities

This paper is concerned with the H
_∞
filtering problem for discrete-time Markovian jump singularly perturbed systems (MJSPSs) with mode-dependent singularly perturbation parameters and partly unknown transition probabilities. Different from the traditional methods, some novel techniques are used to study the stability of MJSPSs. Sufficient conditions for an H
_∞
filter without any singularly perturbation parameters are given in terms of linear matrix inequalities (LMIs) with equality constraints. Finally, an illustrative example is presented to show the effectiveness of the proposed approach.