Finite-time boundedness and finite-time weighted L₂-gain analysis for a class of neutral type switched systems with time-varying delays

ABSTRACT

In this paper, finite-time boundedness of a class of neutral type switched systems with time-varying delays is investigated. By virtue of linear matrix inequalities, delay-depended sufficient conditions are given to guarantee switched systems with time-varying delays finite-time bounded. If there is no disturbance, finite-time boundedness degenerates into finite-time stability, which is also discussed in this note. Mode-depended average dwell time (MDADT) of switching signals is also given such that neutral type switched systems are finite-time bounded or finite-time stable. Moreover, finite-time weighted $L_2$-gain of neutral type switched systems with time-varying delays is presented to measure its disturbance tolerance capability in the fixed time interval. Proofs in detail are accomplished by using multiple Lyapunov–Krasovskii functions. Finally, theoretical results are verified by using a numerical example.

KEYWORDS:

• Switched systems
• linear matrix inequalities (LMIs)
• finite-time boundedness
• mode-depended average dwell time (MDADT)
• multiple Lyapunov–Krasovskii functions

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61773216] and Natural Science Foundation of Jiangsu Province of China [grant number BK20171386].

Notes on contributors

Xiangze Lin

Xiangze Lin graduated from Southeast University, China, in 2000 with the B.S. degree. He received the M.S. degree from Southeast University in 2006 and the Ph.D. degree from Nanjing University of Science and Technology, China, in 2012. He is currently a professor in College of Engineering, Nanjing Agricultural University, China. His research interests include nonlinear control theory, especially finite time boundedeness analysis of switched systems, location and control of agricultural mobile platform.

Zhonglin Yang

Zhonglin Yang received the B.S. degree from Heilongjiang Bayi Agricultural University in 2017, China. He is currently a graduate student in College of Engineering, Nanjing Agricultural University, China. Her research interests include finite-time stability of switched systems.

Shihua Li

Shihua Li graduated from the School of Automation, Southeast University, China, in 1995 with the B.S. degree. He received the M.S. degree and the Ph.D. degree from from the School of Automation, Southeast University respectively in 1998 and in 2001. He is currently a professor at the School of Automation, Southeast University. His main research interests include modeling and nonlinear control theory (nonsmooth control, sliding mode control, disturbance rejection control, adaptive control, etc) with applications to mechatronic systems, including motion control, automobile engine control, manipulator, robot, power electronic systems, etc.