Abstract The main objective of this paper is to study the stability and stabilization problems for a class of impulsive switched systems with inappropriate impulsive switching signals under asynchronous switching. Here, “inappropriate” means that the impulse jump moment may be inconsistent with the asynchronous switching moment or the system switching moment. And “asynchronous” implies that the switching of controller modes lags behind that of system modes. The hybrid case of stable or unstable subsystems combining with stable and unstable impulses is explored. A novel Lyapunov-like function is constructed, which is discontinuous at some special instants, including the switching instants, the instants when the system modes and filter modes are matched, and the impulse jump instants. Based on the novel multiple Lyapunov-like function, the sufficient conditions for the closed loop system to be globally uniformly exponentially stable (GUES) are obtained with admissible edge-dependent switching signals. Furthermore, by excogitating the state-feedback switching controller, the gain matrix of the controller can be obtained by solving the linear matrix inequalities. Finally, two numerical examples and simulation results are given to prove the effectiveness of our main results.

中文翻译：

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异步切换下脉冲切换信号不当的脉冲切换系统的稳定性与稳定性

摘要 本文的主要目的是研究异步切换下一类脉冲切换信号不合适的脉冲切换系统的稳定性和镇定问题。这里的“不合适”是指脉冲跳跃时刻可能与异步切换时刻或系统切换时刻不一致。而“异步”意味着控制器模式的切换滞后于系统模式的切换。探讨了稳定或不稳定子系统与稳定和不稳定脉冲相结合的混合情况。构造了一个新的类李雅普诺夫函数，该函数在一些特殊时刻是不连续的，包括切换时刻、系统模态与滤波器模态匹配的时刻以及脉冲跳跃时刻。基于新颖的多重类李雅普诺夫函数，闭环系统全局一致指数稳定 (GUES) 的充分条件是通过允许的边沿相关开关信号获得的。此外，通过研究状态反馈切换控制器，可以通过求解线性矩阵不等式得到控制器的增益矩阵。最后，给出了两个数值算例和仿真结果来证明我们主要结果的有效性。