Cheng Lei, Xu Xiaozeng, Xue Yuxi, Zhang Hongbin
School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, PR China.
ISA Trans. 2021 Aug;114:99-105. doi: 10.1016/j.isatra.2020.12.031. Epub 2021 Jan 6.
This paper concentrates on the problem of continuous-time switched linear systems with all subsystems unstable under average dwell time (ADT) criteria. Inspired by the matrix polynomial approach, a new method is proposed to further lessen conservativeness and improve system performance. The new method is based on a matrix polynomial and the discretized Lyapunov function (DLF) technique. Using the matrix polynomial, the DLF is successfully established and applied to switched systems. Based on this function, convex sufficient conditions are derived, thereby ensuring the global uniform exponential stability of the system. In addition, the method can be expanded to uncertain systems. Finally, a numerical example is presented to illustrate the potential of the proposed approach.
本文聚焦于平均驻留时间（ADT）准则下所有子系统均不稳定的连续时间切换线性系统问题。受矩阵多项式方法的启发，提出一种新方法以进一步降低保守性并改善系统性能。该新方法基于矩阵多项式和离散化李雅普诺夫函数（DLF）技术。利用矩阵多项式，成功建立了DLF并将其应用于切换系统。基于此函数，推导了凸充分条件，从而确保系统的全局一致指数稳定性。此外，该方法可扩展至不确定系统。最后，给出一个数值例子以说明所提方法的潜力。
