LMI based stability and stabilization for uncertain T-S fuzzy fractional order systems

Abstract

Stability and stabilization issues are fundamental to uncertain fuzzy systems, especially fuzzy system with fractional order. Based on the new linear matrix inequality (LMI) criteria of stability and stabilization of fractional order systems, this paper proposes criteria of stability and stabilization for uncertain Takagi-Sugeno (T-S) fuzzy fractional order systems. Through the new criteria in terms of LMI, two kinds of controllers are designed. One method is to design the different controllers for each sub-systems and another is to design the same controller for different sub-systems. The new controllers design methods are more effective and less conservative than the existing results and decrease the complexity of controllers and save the cost. Two numerical simulation examples are provided to illustrate the effectiveness of the proposed method.