Finite‐time stability analysis of a class of discrete‐time switched nonlinear systems with partial finite‐time unstable modes

• Published in: Asian journal of control 2022-01, Vol.24 (1), p.309-319
• Main Authors: Gao, Zairui, Wang, Ziyun, Wu, Xiaojin, Wang, Wencheng, Liu, Yunlong
• Format: Article
• Language: English
• Subjects: discrete‐time switched nonlinear systems; Dwell time; finite‐time stability; Iterative methods; Linear systems; mode‐dependent average dwell time; multiple Lyapunov‐like functions; Nonlinear systems; Stability analysis; Subsystems
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.2465

Plenty of research achievements on finite‐time stability of discrete‐time switched systems have been reported; however, there are a few results referred to finite‐time unstable subsystems. The design of the average dwell time was not considered alone for finite‐time unstable subsystems in the existing literature. The problems of finite‐time stability and finite‐time boundedness are investigated respectively for a class of discrete‐time switched nonlinear systems with partial finite‐time unstable modes. By using multiple Lyapunov‐like functions, sufficient conditions are derived respectively to ensure that such systems are finite‐time stable and finite‐time bounded based on an improved mode‐dependent average dwell time and iteration technique. Depending on the above results, sufficient conditions, which can guarantee discrete‐time switched linear systems finite‐time stable and finite‐time bounded, are obtained respectively by using matrix inequalities. Finally, numerical examples are given to verify the effectiveness of the proposed methods.