Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information

This paper is concerned with the problem of H∞H∞ filtering for a class of two-dimensional Markovian jump linear systems described by the Fornasini–Marchesini local state-space model. The systems under consideration are subject to state-delays and deficient mode information in the Markov chain. The description of deficient mode information is comprehensive that simultaneously includes the exactly known, partially unknown and uncertain transition probabilities. By invoking the properties of the transition probability matrix, together with the convexification of uncertain domains, a new H∞H∞ performance analysis criterion for the filtering error system is firstly derived. Then, via some matrix inequality linearisation procedures, two approaches for the filter synthesis are proposed. It is shown that both the full-order and reduced-order filters can be constructed by solving a set of linear matrix inequalities. Finally, simulation studies are provided to illustrate the effectiveness of the proposed design methods.