T-S fuzzy control of time-delay systems using multiple Lyapunov functions

This paper investigates the nano-positioning control for a piezoelectric actuator system with states time-delay via multiple Lyapunov functions. The multiple Lyapunov functions can relax stabilization conditions derived by the traditional single Lyapunov function. First, the Bouc-Wen equation establishes the mathematical model of a piezoelectric actuator system. To reduce the nonlinear hysteresis effect, the Bouc-Wen model is linearized by Takagi-Sugeno (T-S) fuzzy systems. According to the proposed stability theorem, we find the feasible solutions of feedback gains by LMIs and employ the strategy of parallel distributed compensation (PDC) to control the piezoelectric actuator system.