Hybrid control for non-overshooting step responses of linear systems

Abstract

This paper focuses on the problem of applying hybrid control to overcome overshoot performance limitations of linear time-invariant (LTI) systems, and puts forward a systematic method for the joint design of a hybrid controller. By modeling the whole closed-loop system in the framework of a hybrid system, an input-to-state stable (ISS) criterion for the system is established, and on the basis of this, conditions for non-overshooting step responses are obtained. In the proposed hybrid controller, apart from its input and output information, state information of the LTI plant and a basic LTI controller is used to design flow and jump sets. The advantage is that when the trigger matrix of flow and jump sets is unknown, it can be designed conveniently. Based on the conditions, the hybrid controller synthesis is formulated in linear matrix inequalities and the algorithm of solving controller matrices and the triggering matrix is given. In addition, the design method of the hybrid controller with a certain triggering matrix is derived. The effectiveness and reliability of the obtained results are demonstrated through a numerical example.