Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information
This paper is concerned with the problem of \(\mathscr {H}_{\infty }\) model approximation for a class of two-dimensional (2-D) discrete-time Markovian jump linear systems with state-delays and imperfect mode information. The 2-D system is described by the well-known Fornasini-Marchesini local state-space model, and the imperfect mode information in the Markov chain simultaneously involves the exactly known, partially unknown and uncertain transition probabilities. By using the characteristics of the transition probability matrices, together with the convexification of uncertain domains, a new \(\mathscr {H}_{\infty }\) performance analysis criterion for the underlying system is firstly derived, and then two approaches, namely, the convex linearisation approach and iterative approach, to the \(\mathscr {H}_{\infty }\) model approximation synthesis are developed. The solutions to the problem are formulated in terms of strict linear matrix inequalities (LMIs) or a sequential minimization problem subject to LMI constraints. Finally, simulation studies are provided to illustrate the effectiveness of the proposed design methods.
model approximation markovian jump systems state-delays imperfect mode information two-dimensional systems