离散多平衡点正切换系统有限区间稳定与镇定
Stability and stabilization for discrete-time positive switched multiple equilibria systems on finite time intervals

在切换事件中, 外界环境的干扰或者事物自身的发展变化会导致多平衡点现象. 此时, 多平衡点切换系统模型比传统的切换系统模型更适合描述此类事件. 因此本文研究离散多平衡点正切换线性系统在有限时间区间上的稳定性与镇定性. 第一, 给出离散多平衡点线性切换系统为正的充要条件. 第二, 提出离散多平衡点正切换线性系统在有限时间区间上稳定的概念. 第三, 通过构造合适的Lyapunov函数以及合理分配系统的驻留时间与切换次数, 针对部分子系统不稳定的离散多平衡点正切换线性系统, 建立所考虑的自治系统有限时间稳定的充分条件. 第四, 给出非自治多平衡点正切换线性系统的控制器设计. 最后, 仿真例子验证理论结果的正确性.
The interference of the external environment or the development and changes of things will lead to the phenomenon of multiple equilibria in the switching events. Compared with the model of general switched systems, the model of multiple equilibria switched systems are better to describe these situations. This paper studies the stability and stabilization for discrete-time multiple equilibria positive switched systems (DT-MEPSSs) on finite time intervals. Firstly, the necessary and sufficient condition of positivity for the switched multiple equilibria systems is proposed. Secondly, the definition of finite time stability for the MEPSSs is given. Thirdly, by establishing a suitable Lyapunov function and managing the dwell time and the number of switching times, a sufficient condition of finite time stability for the DT-MEPSS with unstable subsystems is provided. Fourthly, the controller design for the non-autonomous MEPSS is presented. Finally, a simulation example is given to verify the correctness of the obtained results.