Extended dissipativity and dynamical output feedback control for interval type-2 singular semi-Markovian jump fuzzy systems

Abstract

This paper considers the problems of stochastic admissibility and extended dissipativity analysis, as well as dynamical output feedback controller design for interval type-2 singular semi-Markovian jump fuzzy systems. By utilising the partition method and the matrix decomposition technique, an improved approach of handling the time-varying transition rates is proposed. Based on this approach, a sufficient condition with less conservatism is established to guarantee that the closed-loop system is regular, impulse-free, exponentially stable in mean square and extended dissipative. Determining the parametric matrices of the controller via the obtained sufficient condition is difficult, since some parametric matrices factor between two nonsquare matrices. A dynamical output feedback control scheme is proposed by utilising a vital result which is proposed inspired by Projection lemma. It is worth noting that no conservatism is introduced in controller design due to the sufficiency and necessity of this result. Finally, simulation examples are given to show the effectiveness of the proposed scheme.