Robust Passivity Control for 2-D Uncertain Markovian Jump Linear Discrete-Time Systems

This paper discusses the problem of robust controller design for two-dimensional (2-D) Markovian jump linear systems. The problem is demonstrated using Fornasini-Marchesini local state-space models, which are affected by uncertainties. The transition-mode probability matrix is homogenous and known. It is assumed that the mode information is available for the controller design and implementation. Then, a mode-dependent state-feedback controller is proposed. By substituting the controller into the 2-D system, a stochastic closed-loop system is obtained, because the stochastic variable, external disturbance, and uncertainties are all included in the closed-loop system. Based on the analysis results, an approach to design the controller and its gains is proposed, and the gains are calculated by solving linear matrix inequalities. In section V, a 2-D case is used to verify the performance of the controller.