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This paper tackles a problem of verifying stability of retarded dynamical networks in a dissipative formulation. Subsystems are assumed to be integral input-to-state stable (iISS). Time-delays are allowed to reside in both subsystems and interconnection channels, and may be both discrete and distributed. No assumption is made on the interconnection topology. A small-gain methodology is developed for...
This paper considers interconnected retarded nonlinear systems. Integral input-to-state stable subsystems and the construction of Lyapunov–Krasovskii functionals for their interconnections are focused on. Both discrete and distributed time-delays in the subsystems and the communication channels are covered. This paper provides a sufficient small-gain type condition for the stability of the interconnected...
This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain...
In this paper, interconnected retarded nonlinear systems are considered. Both the constant discrete and distributed time-delays in the subsystems and the interconnections are addressed. A sufficient small-gain type condition for integral input-to-state stability with respect to external inputs is provided in the framework of Lyapunov-Krasovskii functionals.
This paper investigates necessary conditions for stability of nonlinear systems made of feedback interconnection of two iISS subsystems. The integral input-to-state stability (iISS) is a dissipative property which includes the input-to-state stability (ISS) as a special case. It is proved that at least one subsystem needs to be ISS for global asymptotic stability of the feedback loop when two subsystems...
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