Relaxed Resilient Fuzzy Stabilization of Discrete-Time Takagi–Sugeno Systems Based on A New Switching Mechanism

This article investigates the relaxed resilient fuzzy stabilization problem for discrete-time Takagi–Sugeno (T–S) systems based on a new switching mechanism. First, a multimode switching fuzzy controller is constructed, which covers all the possible working modes of system dynamics. For the purpose of reducing conservatism, additional groups of gain matrices are introduced corresponding to different switching modes such that the switching controller switches along with the working modes. Then, the resilient fuzzy stabilization can be accomplished by the proposed controller when the condition of alarm threshold is satisfied. Second, regarding controller design, few groups of time-variant balanced matrices (TVBM) coping with different switching modes are introduced to update the linear matrix inequality (LMI) conditions for system stabilization. Thereby, the feasibility of LMI conditions can be enhanced by using the TVBMs to adjust the related matrix terms in the framework of the homogeneous polynomial technique. Therefore, larger feasible region and less conservatism can be attained by the developed switching mechanism than before even if the alarm threshold is assigned larger values. Finally, a benchmark example is provided to testify the effectiveness and superiority of the proposed method.