Optimal Switched Law of Switched Linear Systems Based on Convergence Direction

A study of optimal switched strategy of switched linear systems in periodic switching is presented here. On the premise that linear switched systems are convergent, optimal switched law is searched to make systems converge at origin in the optimal movement direction. To determine the optimal switched law only requires resolving matrix equation, and the construction of the equation is very simple and precise. Once the optimal switched law is determined, its calculation and configuration form are simple and straightforward. Our simulation examples show that the presented method is simple and effective. At the same time, switched signals designed by the current approach are also very simple. It is in favor of practice application in engineering. The method concluded here can be directly adopted in many kinds of control system design, and it has greate value for both theory and practice.