Stability analysis of complex dynamical systems. Some computational methods

DOI10.1007/BF01600051zbMath0493.93040OpenAlexW188740276MaRDI QIDQ1168936

N. R. Sarabudla, Richard K. Miller, Anthony N. Michel

Publication date: 1982

Published in: Circuits, Systems, and Signal Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01600051

zbMATH Keywords

comparison principlelinearizationdomain of attractionquadratic Lyapunov functionsnonlinear autonomous systemcomputer optimizationnorm type Lyapunov functionsstable critical point

Mathematics Subject Classification ID

Related Items (16)

Using linear feedback laws to augment the quadratic estimates of the stability region of a non-linear system ⋮ A novel LMI-based optimization algorithm for the guaranteed estimation of the domain of attraction using rational Lyapunov functions ⋮ Exact determination of a Lyapunov function and the asymptotic stability domain ⋮ Nonlinear system stability boundary approximation by polytopes in state space† ⋮ On expansion of estimated stability region: theory, methodology, and application to power systems ⋮ Robust optimisation with normal vectors on critical manifolds of disturbance-induced stability loss ⋮ A method for construction of stability regions by Lyapunov functions ⋮ LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems ⋮ On the region of attraction of nonlinear quadratic systems ⋮ Stability regions for constrained nonlinear systems and their functional characterization via support-vector-machine learning ⋮ Analysis of global behaviors in a classical power system ⋮ Some properties of Lyapunov function sets ⋮ Forms of aggregation of nonlinear systems. Domains of asymptotic stability (review) ⋮ Lyapunov function construction for ordinary differential equations with linear programming ⋮ Review on computational methods for Lyapunov functions ⋮ Computation of local ISS Lyapunov functions with low gains via linear programming

Cites Work

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• Qualitative analysis of large scale dynamical systems
• A computational method for determining quadratic Lyapunov functions for non-linear systems
• Stability of dynamical systems: A constructive approach
• Constructive stability and asymptotic stability of dynamical systems
• The behaviour of optimal Lyapunov functions
• Lyapunov stability of interconnected systems: Decomposition into strongly connected subsystems
• Über die Invarianz der Stabilität bei einem Phasenraum-Homöomorphismus.
• Über stabilitätserhaltende Abbildungen und Ljapunovsche Funktionen.

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