Combining iISS and ISS With Respect to Small Inputs: The Strong iISS Property

Abstract : This paper studies the notion of Strong iISS, which is defined as the combination of input-to-state stability (ISS) with respect to small inputs, and integral input-to-state stability (iISS). This notion char- acterizes the robustness property that the state remains bounded as long as the magnitude of exogenous inputs is reasonably small, but may diverge for stronger disturbances. We provide several Lyapunov-based sufficient conditions for Strong iISS. One of them relies on iISS Lyapunov functions admitting a radially non-vanishing (class K) dissipation rate. Although such dissipation inequality appears natural in view of the existing Lyapunov characterization of iISS and ISS, we show through a counter-example that it is not a necessary condition for Strong iISS. Less conservative conditions are then provided, as well as Lyapunov tools to estimate the tolerated input magnitude that preserves solutions’ boundedness.
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Antoine Chaillet, David Angeli, Hiroshi Ito. Combining iISS and ISS With Respect to Small Inputs: The Strong iISS Property. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2014, 59 (9), pp.2518-2524. ⟨10.1109/TAC.2014.2304375⟩. ⟨hal-01103296⟩



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