H∞ control of periodic piecewise vibration systems with actuator saturation

In this paper, an H∞ controller with actuator saturation consideration is proposed to attenuate the vibration of periodic piecewise vibration systems. Based on a continuous Lyapunov function with a time-varying Lyapunov matrix, the H∞ performance index of periodic piecewise vibration systems is studied first. On the basis of the obtained H∞ criterion, the conditions of designing a state-feedback active vibration controller are proposed in matrix inequality form with actuator saturation taken into account. Because of the nonconvexity of the conditions, a corresponding algorithm to compute the controller gain is developed as well. A representative numerical example is used to verify the effectiveness of the proposed method.