Regularity of Liapunov functions for stable systems

DOI10.1016/S0167-6911(00)00062-1zbMath0980.93071MaRDI QIDQ1589495

Lionel Rosier, Andrea Bacciotti

Publication date: 12 December 2000

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

zbMATH Keywords

stabilityregularityLyapunov functionsone-dimensional casetime-invariant systems

Mathematics Subject Classification ID

Lyapunov and storage functions (93D30)

Related Items (10)

Stability in the continuous case ⋮ On the relationship between the \textit{energy shaping} and the \textit{Lyapunov constraint based} methods ⋮ Dual approach to Lyapunov stability ⋮ Introducing some classes of stable systems without any smooth Lyapunov functions ⋮ Lyapunov theorems for systems described by retarded functional differential equations ⋮ Stability analysis of planar systems with nilpotent (non-zero) linear part ⋮ A converse Lyapunov theorem for non-uniform in time, global exponential robust stability ⋮ Input-to-state stability and interconnections of discontinuous dynamical systems ⋮ Lyapunov function design for finite-time convergence analysis: ``twisting controller for second-order sliding mode realization ⋮ Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in \(H_{\infty}\) control

Cites Work

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• Algebraic criteria for the existence of analytic first integrals
• Smooth Lyapunov functions for discontinuous stable systems
• Strong solutions in \(L^ 1\) of degenerate parabolic equations
• Prolongations and stability in dynamical systems
• Liapunov functions and stability in control theory

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