More Relaxed Non‐Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties

Abstract

AbstractThis paper proposes more relaxed stabilization conditions based on a non‐quadratic Lyapunov function (NQLF) and parallel distributed compensator (PDC) controller. The conditions are derived in terms of linear matrix inequalities (LMIs) by introducing three slack matrices based on the properties of TS membership functions, an open loop system and a PDC controller. These slack matrices are utilized to decouple the LMI variables from the TS system and the input matrices. Therefore, the proposed approach greatly reduces the number of LMI conditions and improves feasibility by providing more degrees of freedom compared to recently published studies. Moreover, local stability and stabilization conditions are considered to handle the time derivatives of membership functions appearing in the stabilization synthesis of the TS closed‐loop system with PDC controller. Finally, several examples are presented to demonstrate the advantages of the proposed approaches.