Robust observer-based output feedback control for fuzzy descriptor systems

This paper proposes a robust observer-based output feedback control for fuzzy descriptor systems. First, we represent singular nonlinear dynamic system into Takagi–Sugeno (T–S) fuzzy descriptor model which have a tighter representation for a wider class of nonlinear systems in comparison to general state-space models. To achieve the control objective, we design a fuzzy controller and observer in a unified and systematic manner. The stability analysis of the overall closed-loop fuzzy system leads to formulation of linear matrix inequalities (LMIs). The advantages of the approach are three fold. First, we consider conditions of immeasurable states which allows a practical design of sensorless control systems. Secondly, we address the robustness issue in the system which avoids control performance deterioration or instability due to disturbance or approximation errors in the system. Third, we formulate the overall control problem into LMIs. Using the observer and controller gains by solving LMIs, we carry out numerical simulations which verify theoretical statements.

► A Takagi–Sugeno (T–S) fuzzy model represents a singular nonlinear system into a fuzzy descriptor system. ► A fuzzy observer design estimates immeasurable state. ► An output feedback controller design guarantees H∞ control performance for the overall system. ► Using Lyapunov’s stability analysis, we obtain sufficient conditions for stability of estimation, control, and robustness. ► Observer and controller gains are obtained by solving LMIs.