## 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:

 93D25 Input-output approaches in control theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C10 Nonlinear systems in control theory
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