This paper investigates the stabilization problem for switched linear systems with all modes unstable via designing switching laws. By introducing an associated system whose stability ensures that the original switched system is stable, novel sufficient conditions for the stability of switched systems are proposed. Based on the obtained stability conditions, an effective periodical switching law design strategy is proposed. Compared with the existing strategies which analyze the stability based on the preset dwell time, the admissible dwell times for different subsystems can be calculated efficiently based on the proposed stability conditions. Finally, two examples are provided to illustrate the effectiveness of the proposed strategy.

本文通过设计开关定律研究了具有所有模式不稳定的开关线性系统的稳定性问题。通过引入其稳定性确保原始交换系统稳定的相关系统，提出了用于交换系统稳定性的新颖的充分条件。基于获得的稳定性条件，提出了一种有效的周期切换律设计策略。与现有的基于预设停留时间来分析稳定性的策略相比，可以根据所提出的稳定性条件有效地计算出不同子系统的容许停留时间。最后，提供了两个例子来说明所提出策略的有效性。