ℋ∞Control for Two-Dimensional Markovian Jump Systems with State-Delays and Defective Mode Information

Abstract

This paper investigates the problem of H ∞ state-feedback control for a class of two-dimensional (2D) discrete-time Markovian jump linear time-delay systems with defective mode information. The mathematical model of the 2D system is established based on the well-known Fornasini-Marchesini local state-space model, and the defective mode information simultaneously consists of the exactly known, partially unknown, and uncertain transition probabilities. By carefully analyzing the features of the transition probability matrices, together with the convexification of uncertain domains, a new H ∞ performance analysis criterion for the underlying system is firstly derived, and then the H ∞ state-feedback controller synthesis is developed via a linearisation technique. It is shown that the controller gains can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to verify the effectiveness of the proposed design method.

Probability-Guaranteed $H$_∞-Filtering for 2$D$-Systems with Random Nonlinearities and Missing Measurements

“…Two-dimensional systems with information propagation in two independent directions have attracted considerable attention due to applications in image data processing and transmission, biomedical imaging processing, multidimensional digital filtering, thermal processes, and water stream heating [2,6,10]. In particular, for 2D-systems asymptotic and exponential stability are studied in [24], controller design problems in [4,16], stability analysis and stabilisation of switched systems in [1,21], and H ∞ -control problems for Markovian jump systems with state-delays and defective mode information in [20]. There are also results concerning the H ∞ -filtering design approach -e.g.…”