H/sub ∞/ control for Markovian jump nonlinear systems

Abstract

The problem of disturbance attenuation with internal stability for nonlinear systems with Markovian jumping parameters is considered. It is shown that this problem is solvable if there exists a set of smooth positive semi-definite functions satisfying certain Hamilton-Jacobi-Isaacs inequalities. Furthermore, it is shown that if this solution exists, it represents a stochastic Lyapunov function for the closed-loop nonlinear system.