Stability conditions for some classes of time-varying switched systems

Abstract

In the paper, some classes of time-varying nonlinear switched systems are considered. The stability problem is investigated. The Lyapunov direct method and the theory of differential inequalities are used. The non-stationary switched comparison equation with hybrid degrees is constructed for the considered system. Switching in the comparison equation can be caused by changing the operating modes, as well as changing non-stationary parameters of the system. Sufficient conditions of the asymptotic and finite-time stability are obtained. The region of attraction for the given equilibrium position is estimated. Some examples are presented to illustrate the results. In particular, some classes of nonlinear mechanical system are studied.

Keywords:

• Time-varying switched systems
• stability
• Lyapunov functions
• nonlinear differential inequalities

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Disclosure statement

The author declares that he has no conflict of interest.

Additional information

Notes on contributors

A. V. Platonov

A. V. Platonov received his Ph.D. degree in Mathematics from Saint Petersburg State University, Saint Petersburg, Russia, in 2001. After that, he started to work in this university. In the present time, he holds the position of Associate Professor at the Faculty of Applied Mathematics and Control Processes, Department of Medical and Biological Systems Control. His main research interests include the control theory and the theory of stability. Special attention in the investigations is devoted to the development of methods for the analysis of complex, nonlinear, hybrid dynamical systems. He is the author of about 100 scientific papers.