Absolute Stability Conditions for Switched Positive Coupled Systems with Delays

Abstract

The paper addresses the problem of stability analysis of a switched positive coupled system that describes the interaction of a nonlinear differential subsystem with nonlinearities of a sector type and a linear functional difference one. The case is studied where the considered system contains both point-wise and distributed delays. A special construction of a diagonal Lyapunov–Krasovskii functional is suggested that allows for deriving new absolute stability conditions, i.e., conditions under which the zero solution of the system is asymptotically stable for any admissible nonlinearities and any admissible switching signal. These conditions are formulated in terms of solvability of a system of linear algebraic inequalities. A constructive approach for finding the Lyapunov–Krasovskii functional parameters via the solution of the above inequalities is proposed. In addition, a discrete-time counterpart of a switched positive coupled system is considered. Constraints on the digitization step and the system parameters are obtained under which the discrete-time system is absolutely stable, as well. An illustrative example is given to demonstrate the application of the developed approaches.