Reduced-order H∞ filtering for linear systems with Markovian jump parameters

This paper addresses the reduced-order H∞ filtering problem for continuous-time Makovian jump linear systems, where the jump parameters are modelled by a discrete-time Markov process. Sufficient conditions for the existence of the reduced-order H∞ filter are proposed in terms of linear matrix inequalities (LMIs) and a coupling non-convex matrix rank constraint. In particular, the sufficient conditions for the existence of the zero-order H∞ filter can be expressed in terms of a set of strict LMIs. The explicit parameterization of the desired filter is also given. Finally, a numerical example is given to illustrate the proposed approach.