Observer-based exponential stabilization of Takagi–Sugeno fuzzy systems with state and input delays

This paper proposes an exponential stabilization control method for uncertain Takagi–Sugeno fuzzy systems with state and input delays via output feedback. First, a unified memoryless fuzzy observer-based control method is introduced for stabilizing continuous and discrete uncertain time-delay fuzzy systems. Then, the exponential stability conditions are derived and converted to solving linear matrix inequality (LMI) problems. Based on the developed novel LMI algorithms, the controller and observer gains are able to be separately designed even in the presence of modelling uncertainty, state delay, and input delay. In comparison with existing techniques the proposed technique produces controlled states and state estimation errors that are guaranteed to exponentially converge to zero via output feedback. This is a major breakthrough for the control of uncertain systems with both state and input unavailable time-varying delays. Finally, two studies are carried out on continuous and discrete time-delay systems. Numerical simulation and comparison results demonstrate the quality of the obtained performance.