Static Output Feedback Control Design for Takagi-Sugeno Descriptor Fuzzy Systems

An output feedback control design is an important problem for practical systems because some of the state variables may not measured and hence, a controller with state feedback is not feasible. Here, we are concerned with a new control design method via non-quadratic static output feedback control for fuzzy descriptor systems. Practical systems that are often modeled as a nonlinear system can be expressed by fuzzy descriptor systems. Such systems can describe nonlinear systems with equality constraints. For them, a control design method of admissible non-quadratic static output feedback controllers based on new design conditions is proposed. These conditions result from multiple Lyapunov matrix method and are relatively relaxed, and consequently they can be applied to a broader class of fuzzy descriptor systems. Admissibility conditions and admissible control design conditions are derived via Linear Matrix Inequalities(LMIs) with some given scalar and matrices. At the end, a simple simulation is provided to clarify our method. Main Contribution A new Lyapunov function is introduced to reduce conservatism in control design conditions.