Robust Performance Rule Design for Stochastic Nonlinear Systems with Model Uncertainty

This paper develops the theory of robust performance rule from the view of dissipation to deal with a large class of stochastic nonlinear systems with model uncertainty. In particular, we introduce the notion of dissipation associated with deterministic nonlinear systems to the uncertain stochastic nonlinear systems, and utilize it as a basis for the development of H_infin control. After discussing the properties of dissipation, on the basis of exact stochastic nonlinear systems, we establish the connection between the L₂, -gain of the uncertain stochastic nonlinear systems and the solution to a certain HJI inequality. Owing to the difficulty of the HJI partial differential equation, we consider the robust performance rule problem of the model satisfying some proper matching condition.In the situation,we can obtain the H_infin control law of the system without solving the HJI equation.