Asymptotic stability equals exponential stability, and ISS equals finite energy gain -- if you twist your eyes.

DOI10.1016/S0167-6911(99)00053-5zbMath1043.93549arXivmath/9812137OpenAlexW2058758497MaRDI QIDQ1606516

Lars Grüne, Fabian R. Wirth, Eduardo D. Sontag

Publication date: 24 July 2002

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9812137

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Asymptotic stability in control theory (93D20) Stability of solutions to ordinary differential equations (34D20)

Related Items (16)

Stability and stabilization of linear positive systems on time scales ⋮ A system-theoretic framework for a wide class of systems. I: Applications to numerical analysis ⋮ Further results on strict Lyapunov functions for rapidly time-varying nonlinear systems ⋮ Stochastic approximation with long range dependent and heavy tailed noise ⋮ Linearization in the large of nonlinear systems and Koopman operator spectrum ⋮ The exponential input-to-state stability property: characterisations and feedback connections ⋮ Growth conditions for global exponential stability and exp-ISS of time-delay systems under point-wise dissipation ⋮ An invariance kernel representation of ISDS Lyapunov functions ⋮ Nonlinear \(\mathcal{L}_2\)-gain verification for nonlinear systems ⋮ Min-max model predictive control of nonlinear systems: a unifying overview on stability ⋮ Noncoercive Lyapunov Functions for Input-to-State Stability of Infinite-Dimensional Systems ⋮ Non-coercive Lyapunov functions for infinite-dimensional systems ⋮ Convergence rates of perturbed attracting sets with vanishing perturbation ⋮ Qualitative equivalences of ISS and \(l_p\)-gain stability properties for discrete-time nonlinear systems ⋮ Performance bounds for nonlinear systems with a nonlinear ℒ₂-gain property ⋮ On Hamilton-Jacobi approaches to state reconstruction for dynamic systems

Cites Work

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