一类离散时间切换线性系统的无差拍控制

研究一类带多控制器和多传感器离散时间线性系统的无差拍控制.对能控系统,通过适当的状态坐标变换获得系统矩阵的块三角结构,再设计状态反馈和周期切换策略使得状态反馈矩阵在有限周期内为零,从而保证闭环系统的无差拍稳定.进一步,对能观系统,设计具有有限时间精确估计的动态输出反馈,通过适当的周期切换策略实现闭环系统的无差拍稳定.最后,给出一个例子以验证所提设计方法的有效性.

Deadbeat control for a class of discrete-time switched linear systems

This article addresses the deadbeat stabilization problem for a class of discrete-time linear systems with multiple actuators and multiple sensors. For switched controllable systems, blocked triangular structure of the system matrix is obtained via proper state coordinate transform. Based on this specific matrix structure, we design a set of state-feedback controllers and a periodic switching signal to coordinate the controllers. The state transition matrix is proved to be zero within a fixed time interval, and hence the deadbeat stabilization problem is solved in a global and uniform manner. Furthermore, for switched observable systems, we design an observer that exactly traces the state in a finite time. Combined the state feedback controller and the observer, we propose a dynamical output feedback controller that is itself a switched system. This dynamic controller, together with a periodic switching signal, could achieve deadbeat stability of the overall system. A numerical example is presented to illustrate the effectiveness of the proposed design scheme.