ISDS small-gain theorem and construction of ISDS Lyapunov functions for interconnected systems

DOI10.1016/j.sysconle.2010.03.004zbMath1191.93125OpenAlexW2135425479MaRDI QIDQ976193

Lars Naujok, Sergey N. Dashkovskiy

Publication date: 17 June 2010

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

Full work available at URL: https://doi.org/10.1016/j.sysconle.2010.03.004

zbMATH Keywords

nonlinear systemsinterconnected systemssmall-gain conditioninput-to-state dynamical stability (ISDS)ISDS Lyapunov function

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Input-output approaches in control theory (93D25) Control problems involving ordinary differential equations (34H05) Large-scale systems (93A15)

Related Items (7)

Robust Stability Analysis for Uncertain Time-Delay System ⋮ Lyapunov-Krasovskiĭ functionals and application to input delay compensation for linear time-invariant systems ⋮ MPC schemes guaranteeing ISDS and ISS for nonlinear (time-delay) systems ⋮ Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions ⋮ Novel criteria for exponential stability of functional differential equations ⋮ Input-to-state-stability-type comparison principles and input-to-state stability for discrete-time dynamical networks with time delays ⋮ Quasi-ISS/ISDS observers for interconnected systems and applications

Cites Work

• Asymptotic behavior of dynamical and control systems under perturbation and discretization
• Small-gain theorem for ISS systems and applications
• A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems
• Constructive nonlinear control
• An ISS small gain theorem for general networks
• A characterization of integral input-to-state stability
• New characterizations of input-to-state stability
• Smooth stabilization implies coprime factorization
• Input-to-state dynamical stability and its Lyapunov function characterization

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