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Zbl 0979.93106
Angeli, David; Sontag, Eduardo D.; Wang, Yuan
A characterization of integral input-to-state stability. (English)
[J] IEEE Trans. Autom. Control 45, No.6, 1082-1097 (2000). ISSN 0018-9286

The authors present several necessary and sufficient Lyapunov-like characterizations of the integral input-to-state stability property in terms of dissipation inequalities and a zero-detectability condition allowing the application of the LaSalle invariance principle. The notion of integral intput-to-state stability generalizes the concept of finite gain allowing to quantify sensitivity in the presence of nonlinear resonance. The paper ends with a counter-example which exhibits a forward complete and 0-GAS system which has not the integral intput-to-state stability property.
[Patrick Saint-Pierre (Paris)]

MSC 2000:: *93D25 Input-output approaches to stability of control systems
93D05 Lyapunov and other classical stabilities of control systems
93C10 Nonlinear control systems

Keywords: input-to-state stability; nonlinear systems; tracking; dissipation inequalities; LaSalle invariance principle

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