H2 guaranteed cost of uncertain continuous T-S fuzzy systems by multiple Lyapunov function approach

In this paper, the H₂ guaranteed cost control problem of uncertain continuous T-S fuzzy systems is investigated. We approach this problem by considering the multiple Lyapunov function and utilizing the non-PDC controller. Sufficient conditions for ensuring certain H₂ cost as well as asymptotical stability are derived and expressed in terms of LMIs. Unlike existing approaches, the assumption of known upper bounds on the time derivative of membership functions, which is quite unrealistic, is not required anymore in the present one. Numerical examples are also given to demonstrate our approach has lower H₂ guaranteed cost as well as control force in comparison with the existing ones.