Robust stabilization and observation for positive takagi-sugeno systems

Résumé

This dissertation proposes methodologies to design robust controllers and observers for positive systems described by uncertain linear and Takagi-Sugeno (T-S) models, maybe with time-delays. The synthesis conditions are expressed as LMIs (Linear Matrix Inequalities). In the first part, conditions are established to guarantee the asymptotic and ¿-stabilization of positive linear and T-S systems, maybe subject to interval uncertainties, by using a decomposed state-feedback controller. In the second part, necessary and sufficient conditions are given for the stabilization of positive T-S systems with time-delay, in two cases: when the premise variables of the system are measurable or not. In addition, the problem of observer-based control design is considered, by state-feedback laws that can be chosen with or without memory. To show the performance of the proposed methods, numerical and practical examples are provided, giving satisfactory results.