Robust Stability and Stabilization of a Class of Nonlinear Ito-Type Stochastic Systems via Linear Matrix Inequalities

This article presents a new approach to robust quadratic stabilization of nonlinear stochastic systems. The linear rate vector of a stochastic system is perturbed by a nonlinear function, and this nonlinear function satisfies a quadratic constraint. Our objective is to show how linear constant feedback laws can be formulated to stabilize this type of stochastic systems and, at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable. The new formulation provides a suitable setting for robust stabilization of nonlinear stochastic systems where the underlying deterministic systems satisfy the generalized matching conditions. Our sufficient conditions are written in matrix forms, which are determined by solving linear matrix inequalities (LMIs), which have significant computational advantage over any other existing techniques. Examples are given to demonstrate the results.