Nonquadratic stabilization conditions for nonhomogeneous Markovian jump fuzzy systems with higher-level operation modes

Abstract

This paper is concerned with the problem of designing a dissipative control for generalized nonhomogeneous Markovian jump fuzzy systems (MJFSs) that can cover both piecewise-homogeneous MJFSs and nonhomogeneous MJFSs through the use of dual modes, i.e., plant and higher-level modes. Based on a dual-mode-dependent fuzzy control law within a nonparallel distributed compensation (non-PDC) scheme, the nonquadratic stabilization conditions are first formulated in terms of multi-parameterized linear matrix inequalities (M-PLMIs), and then be transformed into a finite set of solvable LMIs without reducing M-PLMIs to PLMIs. Further, since the proposed relaxation technique can address the transition probabilities of plant and higher-level modes at once, the characteristics on mutual dependence between dual modes are fully incorporated into the nonquadratic stabilization conditions. Two illustrative examples are given to show the validity of the proposed approach.