Impulse-based controller synthesis for a class of polynomial systems

This paper develops a time-triggered impulsive control strategy for stabilisation problem of a class of polynomial systems. The proposed hybrid control method combines time-triggered impulsive control and state-feedback control. To obtain the control feedback gain, the matrix sum-of-squares programming is employed to solve the feasible solutions of constructed positive polynomial problems. Compared with a single time-triggered impulsive control or the pure state-feedback control, the proposed control method can effectively combine the advantages of the two control methods. In particular, the design of the controller is more flexible and the control effect is greatly improved. Finally, two simulation examples including the Chua's chaotic system are provided to illustrate the effectiveness and superiority of the proposed method.