State feedback fuzzy-model-based control for Markovian jump nonlinear systems

Abstract

This paper deals with the fuzzy-model-based control design for a class of Markovian jump nonlinear systems. A fuzzy system modeling is proposed to represent the dynamics of this class of systems. The structure of the fuzzy system is composed of two levels, a crisp level which describes the Markovian jumps and a fuzzy level which describes the system nonlinearities. A sufficient condition on the existence of a stochastically stabilizing controller using a Lyapunov function approach is presented. The fuzzy-model-based control design is formulated in terms of a set of linear matrix inequalities. Simulation results for a single-machine infinite-bus power system which is modeled as a Markovian jump nonlinear system in the infinite-bus voltage are presented to illustrate the applicability of the technique.