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• W3104949460 abstract "We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs, the existence of an ISS-Lyapunov function implies the ISS of a system. Then for the case of systems described by abstract equations in Banach spaces, we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system, the linear approximation of which is ISS. In order to study the interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations." @default.
• W3104949460 created "2020-11-23" @default.
• W3104949460 creator A5004635071 @default.
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• W3104949460 date "2012-08-28" @default.
• W3104949460 modified "2023-10-18" @default.
• W3104949460 title "Input-to-state stability of infinite-dimensional control systems" @default.
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• W3104949460 doi "https://doi.org/10.1007/s00498-012-0090-2" @default.
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