Dissipative control of interval type-2 nonhomogeneous Markovian jump fuzzy systems with incomplete transition descriptions

Abstract

This paper investigates the problem of designing a dissipative controller for interval type-2 nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition descriptions. To explore a generalized model for MJFSs under realistic situations, the coexistence of incompletely known transition rates and mismatched membership functions is considered in MJFS models, and the corresponding stabilization conditions are derived in terms of multi-parameterized linear matrix inequalities (M-PLMIs). In addition, to handle the problem of M-PLMIs, two novel relaxation techniques are additionally proposed such that the use of redundant constraints on multiple time-varying parameters can be significantly reduced. Finally, the validity of the proposed method is demonstrated via two illustrative examples.