Finite and infinite horizon H{infty} control for stochastic nonlinear systems

In this paper, the problem of disturbance attenuation with internalstability for nonlinear systems with Markovian jumping parametersis considered. It is shown that this problem is solvable ifthere exists a sequence of smooth-positive semidefinite functionssatisfying certain Hamilton-Jacobi-Isaac equations (inequalities).Furthermore, it is shown that, if this solution exists, it representsa stochastic Lyapunov function for the closed-loop nonlinearsystem. A parametrization of the family of full-informationstate-feedback controllers satisfying the disturbance-attenuationrequirement with stochastic stability for the closed-loop systemis also given.