Stability of totally-positive switched linear systems with mode-dependent average dwell time switching

Totally-positive switched linear systems (TSLSs), as one of the special switched system classes, have both the complex dynamic behavior of switched systems and their special dynamic properties of totally positive dynamical systems. Recently, TSLSs have attracted scientists’ extensive attention, due to their wide applications, such as economics, biology, communication, and electronic information engineering. The research focuses on the stability issue of TSLSs. Several new exponential stability criteria of TSLSs in both continuous-time and discrete-time cases are obtained by combining the strategy of mode-dependent average dwell time (MDADT) and the multiple linear co-positive Lyapunov function approach. Those stability criteria obtained are presented in the form of linear constraints, making them easy to verify and apply through tools such as linear programming (LP). Since the MDADT framework only limits the average dwell time (ADT) of each subsystem and does not impose restrictions on the switching order or subsystem activation frequency, the conclusion of this paper is robust for switching sequences. The corresponding ADT stability criteria have also been inferred. Furthermore, it is pointed out that the stability issue under arbitrary switching can be solved by the common linear co-positive Lyapunov function (CLCLF) method. Finally, the efficiency of the results is verified by two numerical examples. One of them is from the epidemiological models, which provides a practically motivated TSLSs to make the validation more convincing.