Set-valued Lyapunov functions for difference inclusions

DOI10.1016/j.automatica.2010.10.018zbMath1209.93138OpenAlexW2092137102MaRDI QIDQ629060

Rafal Goebel

Publication date: 8 March 2011

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2010.10.018

zbMATH Keywords

asymptotic stabilityconsensuscontinuum of equilibriaconverse Lyapunov resultdifference inclusionset-valued Lyapunov function

Mathematics Subject Classification ID

Lyapunov and storage functions (93D30) Asymptotic stability in control theory (93D20) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30)

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Optimal control for pointwise asymptotic stability in a hybrid control system, Stability and robustness for saddle-point dynamics through monotone mappings, Robustness of stability through necessary and sufficient Lyapunov-like conditions for systems with a continuum of equilibria, Pointwise Asymptotic Stability in a Hybrid System and Well-Posed Behavior Beyond Zeno, Consensus of discrete-time multi-agent systems with transmission nonlinearity

Cites Work

• Stability of leaderless discrete-time multi-agent systems
• Comments on integral variants of ISS
• Variational Analysis
• Nontangency-Based Lyapunov Tests for Convergence and Stability in Systems Having a Continuum of Equilibria
• Smooth Lyapunov Functions for Hybrid Systems Part II: (Pre)Asymptotically Stable Compact Sets
• Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks
• Semistability, Finite-Time Stability, Differential Inclusions, and Discontinuous Dynamical Systems Having a Continuum of Equilibria
• On Conditions for Convergence to Consensus
• Stability of multiagent systems with time-dependent communication links
• On the Robustness of $\mathcalKL$-stability for Difference Inclusions: Smooth Discrete-Time Lyapunov Functions