Zhang Hongbin, Xie Dehua, Zhang Hongyu, Wang Gang
School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu 210049, China; School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
ISA Trans. 2014 Jul;53(4):1081-6. doi: 10.1016/j.isatra.2014.05.020. Epub 2014 Jun 9.
This paper mainly intends to present new stability results of a discrete-time switched system with unstable subsystems. By adopting multiple Lyapunov functions׳ (MLFs׳) method, new and less conservative stability conditions are derived in terms of a set of numerical feasible linear matrix inequalities (LMIs) with mode-dependent average dwell time (MDADT) techniques. Different from previous literatures, unstable subsystems are considered under two situations in this paper. It is shown that the discrete-time switched system can achieve exponential stability under a slow switching scheme and even in the presence of fast switching of unstable subsystems. Finally a numerical example is given to demonstrate the effectiveness of the proposed method.
本文主要旨在给出具有不稳定子系统的离散时间切换系统的新稳定性结果。通过采用多Lyapunov函数（MLFs）方法，借助一组依赖于模式的平均驻留时间（MDADT）技术的数值可行线性矩阵不等式（LMIs），推导出了新的且保守性较低的稳定性条件。与以往文献不同，本文在两种情况下考虑不稳定子系统。结果表明，离散时间切换系统在慢切换方案下甚至在存在不稳定子系统快速切换的情况下都能实现指数稳定性。最后给出一个数值例子以证明所提方法的有效性。
