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Constructions of Strict Lyapunov Functions

2009
The construction of strict Lyapunov functions is a challenging problem that is of significant ongoing research interest. Although converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, the Lyapunov functions that converse theory provides are often abstract and nonexplicit, and therefore may not lend ...
Malisoff, Michael, Mazenc, Frédéric
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Optimum Lyapunov functions [PDF]

Dynamics and Control, 1995
A Lyapunov operator, generated by a stable linear system, is considered. Some problems of optimization on the set of square Lyapunov, functions are stated. These problems are reduced to original games with matrix strategies. The iterative method of optimum Lyapunov function search has been worked out.
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Lyapunov functionals and matrices

Annual Reviews in Control, 2010
Abstract In this contribution we present some basic results concerning the computation of quadratic functionals with prescribed time derivatives for linear time delay systems. Some lower and upper bounds for the functionals are given. The functionals are defined by special matrix valued functions. These functions are called Lyapunov matrices.
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Optimization of lyapunov functionals

Meccanica, 1975
The problem of optimality of Lyapunov Functionals is posed in terms of the requirements of a specific problem. The optimizationprocess is based on a method used to construct Lyapunov Functionals called “Path Integral Synthesis” proposed by the authors.
Carmine Golia, Jacob M. Abel
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On quadratic lyapunov functions

IEEE Transactions on Automatic Control, 2003
A topological structure, as a subset of [0,2/spl pi/)/sup L//spl times//spl Ropf//sub +//sup n-1/, is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral ...
Jie Huang, Daizhan Cheng, Lei Guo
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Lyapunov Functions for Attractors

2017
The concept of global uniform asymptotical stability of a set is defined through Lyapunov stability and uniformly attractivity. Yoshizawa’s Theorem on the existence of a Lyapunov function characterising global uniform asymptotical stability of a compact set is presented.
Peter E. Kloeden, Xiaoying Han
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Lyapunov Functions

1992
Publisher Summary This chapter elaborates the yield and applications of Lyapunov functions. It is applicable to ordinary differential equations and partial differential equations. It yields bounds on the solution in phase space. Even without solving a given differential equation, sometimes one can restrict the solution to be in a certain portion of ...
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Minimization of Lyapunov Functions

2016
In this chapter we give a general overview of utilizing extremum seeking (ES) to stabilize a large class of systems, and discuss the strength of the approach for systems with unknown control directions, providing a stabilizing controller that is more robust than traditional Nussbaum type control.
Miroslav Krstic, Alexander Scheinker
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Lyapunov Functions and Martingales

1999
The present chapter contains a potpourri of topics around potential theory and martingale theory. More exactly, it is a brief introduction to these topics, with the limited purpose of showing the power of martingale theory and the rich interplay between probability and analysis.
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Composite Quadratic Lyapunov Functions

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2003
A Lyapunov function based on a group of quadratic functions is introduced. We call this Lyapunov function a composite quadratic function. Some important properties of this Lyapunov function are revealed. We show that this function is continuously differentiable and its level set is the convex hull of a group of ellipsoids.
Zongli Lin, Tingshu Hu
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