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.

本文重点研究在平均停留时间 (ADT) 标准下所有子系统都不稳定的连续时间切换线性系统的问题。受矩阵多项式方法的启发，提出了一种新方法，以进一步降低保守性并提高系统性能。新方法基于矩阵多项式和离散化李雅普诺夫函数 (DLF) 技术。使用矩阵多项式，DLF 成功建立并应用于切换系统。基于该函数，推导出凸充分条件，从而保证系统全局一致指数稳定性。此外，该方法可以扩展到不确定系统。最后，给出了一个数值例子来说明所提出方法的潜力。