H∞H∞ filtering for two-dimensional continuous-time Markovian jump systems with deficient transition descriptions

This paper investigates the problems of mode-dependent and mode-independent H∞H∞ filtering for a class of continuous-time two-dimensional (2-D) Markovian jump linear systems with deficient transition descriptions. The 2-D systems under consideration are described by the well-known Roesser model and subject to the deficient transition descriptions in the Markov stochastic process, which simultaneously involves the exactly known, partially unknown and uncertain transition rates. By fully exploiting the properties of 2-D cumulative distribution function and transition rate matrices, together with the convexification of uncertain domains, a sufficient condition for H∞H∞ performance analysis is firstly derived, and then both the mode-dependent and mode-independent filter synthesis are developed, respectively. It is shown that via some linearization procedures, a unified framework can be developed such that the H∞H∞ filters can be obtained by solving a set of linear matrix inequalities. Finally, an illustrative example is given to validate the effectiveness of the proposed design methods.