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A characterization of integral input-to-state stability. (English) Zbl 0979.93106
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.
MSC:
93D25Input-output approaches to stability of control systems
93D05Lyapunov and other classical stabilities of control systems
93C10Nonlinear control systems