Liapunov and Lagrange stability: inverse theorem for discontinuous systems

DOI10.1007/BF02741887zbMath0919.34051MaRDI QIDQ1265425

Lionel Rosier, Andrea Bacciotti

Publication date: 31 August 1999

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

zbMATH Keywords

differential inclusionsLagrange and Lyapunov stabilityweak Lyapunov function

Mathematics Subject Classification ID

Ordinary differential inclusions (34A60) Stability of solutions to ordinary differential equations (34D20) Growth and boundedness of solutions to ordinary differential equations (34C11)

Related Items

Stability in the continuous case, Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions, A converse Lyapunov theorem for non-uniform in time, global exponential robust stability, Nonsmooth analysis in control theory: a survey, Asymptotic stability and smooth Lyapunov functions, Regularity of Liapunov functions for stable systems, A smooth Lyapunov function from a class-${\mathcal{KL}}$ estimate involving two positive semidefinite functions, Classical converse theorems in Lyapunov's second method

Cites Work

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• Contributions to stability theory
• Stability theory by Liapunov's direct method
• Small-gain theorem for ISS systems and applications
• Prolongations and stability in dynamical systems
• Stability in general control systems
• Construction of a smooth Lyapunov function for an asymptotically stable set
• On the reversibility of the first theorem of Lyapunov concerning the stability of motion
• The converse theorems of Lyapunov and Persidskij concerning the stability of motion
• Smooth stabilization implies coprime factorization
• A Smooth Converse Lyapunov Theorem for Robust Stability
• Global stability and external stability of dynamical systems
• On the inversion of Ljapunov’s second theorem on stability of motion
• Differential equations with discontinuous right-hand side
• Smoothing Derivatives of Functions and Applications
• Bounded-Input Bounded-Output Stability of Nonlinear Time-Varying Differential Systems
• On the stability of solutions of a system of differential equations