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This paper presents a Lyapunov formulation of the cyclic-small-gain theorem for dynamical networks composed of interconnected discrete-time input-to-state stable (ISS) subsystems. ISS-Lyapunov functions for dynamical networks satisfying cyclic-small-gain are constructed from the ISS-Lyapunov functions of the subsystems.
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.
In this paper, a class of hybrid switched systems with impulsive effects is considered. In light of the conventional input-to-state stability (ISS) and its various extensions (i-ISS, e-ISS and ei-ISS), we propose novel criteria on ISS, i-ISS, e-ISS and ei-ISS for these impulsive switched systems. The obtained results show that an impulsive switched system may be ISS, even when the continuous-time...
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