On the equivalence between asymptotic and exponential stability, and between ISS and finite H/sub /spl infin// gain

Keywords

Exponential stability, Equivalence (formal languages), Mathematics, Nonlinear system, Stability (learning theory)

References

• A Converse Lyapunov Theorem with Applications to Iss-Disturbance Attenuation 1Yuan Wang — 1996
• The topology of four-dimensional manifoldsMichael Freedman — 1982
• Generalized weighted homogeneity and state dependent time scale for linear controllable systemsLaurent Praly — 1997
• Lectures on the h-cobordism theoremJohn Milnor — 1965
• Addendum to: Local trajectory equivalence of differential systemsCourtney Coleman — 1966
• Smooth stabilization implies coprime factorizationEduardo D. Sontag — 1989
• Small-gain theorem for ISS systems and applicationsZ.-P. Jiang, Andrew R. Teel, Laurent Praly — 1994
• Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbationsLars Grüne — 1999
• Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systemsAlberto Isidori, Alessandro Astolfi — 1992
• Global almost disturbance decoupling with stability for non minimum-phase single-input single-outputAlberto Isidori — 1996
• Local trajectory equivalence of differential systemsCourtney Coleman — 1965
• Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyesLars Grüne, Eduardo D. Sontag, Fabian Wirth — 1998
• Singular perturbations and input-to-state stabilityPanagiotis D. Christofides, Andrew R. Teel — 1996
• Comments on integral variants of ISSEduardo D. Sontag — 1998
• A result on robust boundednessJean‐Baptiste Pomet, Laurent Praly — 1988
• The structure of the level surfaces of a Lyapunov functionF. Wilson — 1967
• Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturationJ. Tsinias — 1997
• A Smooth Converse Lyapunov Theorem for Robust StabilityYuandan Lin, Eduardo D. Sontag, Yuan Wang — 1996
• Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stabilityLaurent Praly, Yuan Wang — 1996
• On characterizations of the input-to-state stability propertyEduardo D. Sontag, Yüan Wang — 1995

Cited by

• A Condition for Output-to-State Stability of Switched Nonlinear SystemsMingshun Wang, Georgi M. Dimirovski, Jun Zhao — 2006

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