Construction of Lyapunov functions for nonlinear planar systems by linear programming
type: Item
instance of: scholarly article
title: Construction of Lyapunov functions for nonlinear planar systems by linear programming
zbMATH Open document ID: 1248.34083
author: Peter Giesl
author: Sigurdur Hafstein
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-02-11T00:00:00Z
review text: The authors extend recent results devoted to the construction of piecewise affine Lyapunov functions for planar dynamical systems with an exponentially stable equilibrium. They describe an algorithm based on a linear programming problem whose solution defines a Lyapunov function. It is proved that the algorithm always succeeds in constructing a Lyapunov function for the mentioned systems. The domain of the Lyapunov function is only limited by the region of attraction of the equilibrium.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 6005704
zbMATH Keywords: exponentially stable equilibrium
zbMATH Keywords: piecewise affine Lyapunov function
zbMATH Keywords: triangulation
zbMATH Keywords: linear programming problem
describes a project that uses: Algorithm 432
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.10.047
OpenAlex ID: W1997267116
cites work: Linear programming based Lyapunov function computation for differential inclusions
cites work: Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
cites work: Q3172793
cites work: Construction of global Lyapunov functions using radial basis functions
cites work: Existence of piecewise affine Lyapunov functions in two dimensions
cites work: A constructive converse Lyapunov theorem on exponential stability
cites work: A constructive converse Lyapunov theorem on asymptotic stability for nonlinear autonomous ordinary differential equations
cites work: Q5431011
cites work: Q5584086
cites work: Computation of Lyapunov functions for smooth nonlinear systems using convex optimization
cites work: Computation of piecewise quadratic Lyapunov functions for hybrid systems
cites work: A parametrization of piecewise linear Lyapunov functions via linear programming
cites work: Q3029380
cites work: Lyapunov function construction for ordinary differential equations with linear programming
cites work: Q3195252
cites work: Exponentially Stable Nonlinear Systems Have Polynomial Lyapunov Functions on Bounded Regions
cites work: Nonlinear systems. Analysis, stability, and control
cites work: An introduction to manifolds
cites work: Q5724099
DOI: 10.1016/J.JMAA.2011.10.047
Recommended article: Q3834369
Recommended article: Lyapunov function construction by linear programming
Recommended article: Lyapunov function construction for ordinary differential equations with linear programming
Recommended article: Q3836682
Recommended article: On the construction of Lyapunov functions for nonlinear systems
Recommended article: Q3535927
Recommended article: Q4177901
Recommended article: Construction of Lyapunov functions for a class of systems of nonlinear differential equations
Recommended article: Construction of the Lyapunov function for parametrically perturbed linear systems
Recommended article: Computation of Lyapunov functions for nonautonomous systems on finite time-intervals by linear programming
description: scientific article; zbMATH DE number 6005704