Abstract
In this study, the robust stochastic H infinity reference tracking control design is proposed for stochastic polynomial fuzzy system (SPFS) under external disturbance and continuous and discontinuous random fluctuations. To simplify the tracking control design, the desired reference trajectory is generated by a reference polynomial system. Under the concept of H infinity control, the designed control strategy aims to attenuate the effect of all possible finite energy disturbance on the tracking error to a prescribed level. Based on the polynomial Lyapunov function, with the help of Itô-Lévy formula, the sufficient conditions for robust stochastic H infinity reference tracking control design of SPFS is transformed to Hamilton-Jacobi inequalities (HJIs) problem. Due to the difficulties in solving HJIs problem, by using quadratic Lyapunov function, the solvable sum-of-squares (SOS) conditions are established for the robust stochastic H infinity reference tracking control design and it can be efficiently solved via MATLAB SOSTOOLS toolbox. An investment tracking strategy design for the stochastic financial system is provided to validate the effectiveness of proposed method.