Robust $H_{\mathrm{\infty }}$ output feedback finite-time control for interval type-2 fuzzy systems with actuator saturation

The finite-time $H_{\mathrm{\infty }}$ performance of the interval type-2 Takagi-Sugeno fuzzy system (IT2 T-S) in presence of immeasurable states and input saturation is investigated. At first, an observer associated with IT2 T-S states is considered to address the problem of immeasurable states. After that, the input saturation is described based on the polyhedron model, and accordingly, a robust $H_{\mathrm{\infty }}$ observer-based finite-time controller is proposed via non-PDC algorithm. Then, on the basis of the Lyapunov function method and LMIs theory, the sufficient conditions for the finite time stability of fuzzy systems are derived. At last, the feasibility of the designed algorithm is verified by two examples of the nonlinear mass-spring-damping system and tunnel diode circuit system, respectively.