Robust static output feedback fuzzy control design for a class of nonlinear stochastic systems

Abstract

This paper describes the robust static output feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy control design for a class of nonlinear stochastic systems. The system dynamic is modelled by Itô-type stochastic differential equations. For general nonlinear stochastic systems, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality. In general, it is difficult to solve the second-order nonlinear Hamilton-Jacobi inequality. Using fuzzy approach (T-S fuzzy model), the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy control design for the nonlinear stochastic systems can be given via solving linear matrix inequalities (LMIs) instead of a second-order Hamilton-Jacobi inequality. A singular value decomposition (SVD) method is proposed in this study to solve the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> static output feedback fuzzy control problem. By the proposed SVD method, the problem of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> static output feedback fuzzy control design for nonlinear stochastic systems is characterized in terms of solving an eigenvalue problem (EVP). This EVP can be easily solved by using a LMI-based optimization method. Simulation example is provided to illustrate the design procedure and the expected performances.