Construction of Diagonal Lyapunov–Krasovskii Functionals for a Class of Positive Differential-Algebraic Systems

A coupled system describing the interaction of a differential subsystem with nonlinearitiesof a sector type and a linear difference subsystem is considered. It is assumed that the system ispositive. A diagonal Lyapunov–Krasovskii functional is constructed, and conditions aredetermined under which the absolute stability of the system can be proved with the use of such afunctional. In the case of power-law nonlinearities, estimates for the rate of convergence of thesolution to the origin are obtained. The stability of the corresponding system with parameterswitching is analyzed. Sufficient conditions guaranteeing the asymptotic stability of the zerosolution for any admissible switching law are obtained.