Construction of Lyapunov functions for nonlinear planar systems by linear programming

DOI10.1016/j.jmaa.2011.10.047zbMath1248.34083OpenAlexW1997267116MaRDI QIDQ662089

Peter Giesl, Sigurður Freyr Hafstein

Publication date: 11 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.10.047

zbMATH Keywords

triangulationlinear programming problemexponentially stable equilibriumpiecewise affine Lyapunov function

Mathematics Subject Classification ID

Linear programming (90C05) Stability of solutions to ordinary differential equations (34D20)

Related Items (9)

Computation and Verification of Lyapunov Functions ⋮ What is the most suitable Lyapunov function? ⋮ Computing continuous and piecewise affine Lyapunov functions for nonlinear systems ⋮ Computation of Lyapunov functions for nonlinear discrete time systems by linear programming ⋮ Construction of mean-square Lyapunov-basins for random ordinary differential equations ⋮ Improved algorithm for computing the domain of attraction of rational nonlinear systems ⋮ Revised CPA method to compute Lyapunov functions for nonlinear systems ⋮ Computational method for estimating the domain of attraction of discrete-time uncertain rational systems ⋮ Computation of Lyapunov functions for systems with multiple local attractors

Uses Software

• Algorithm 432

Cites Work

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• Linear programming based Lyapunov function computation for differential inclusions
• Construction of global Lyapunov functions using radial basis functions
• Existence of piecewise affine Lyapunov functions in two dimensions
• Nonlinear systems. Analysis, stability, and control
• A constructive converse Lyapunov theorem on exponential stability
• An introduction to manifolds
• Lyapunov function construction for ordinary differential equations with linear programming
• Computation of piecewise quadratic Lyapunov functions for hybrid systems
• A parametrization of piecewise linear Lyapunov functions via linear programming
• Exponentially Stable Nonlinear Systems Have Polynomial Lyapunov Functions on Bounded Regions
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• A constructive converse Lyapunov theorem on asymptotic stability for nonlinear autonomous ordinary differential equations
• Computation of Lyapunov functions for smooth nonlinear systems using convex optimization

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