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Constructions of Strict Lyapunov Functions
2009The 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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PERSISTENT SETS VIA LYAPUNOV FUNCTIONS
Nonlinear Analysis: Theory, Methods & Applications, 1979A modeler may understand the basic dynamics of a biological system, but there are always some forces, perhaps due to the effects of a random environment, that he does not understand or cannot predict. In this situation it may not be feasible to predict exact trajectories of the system, but it may be important to determine whether the system stays in an
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1999
The main objective of control is to modify the behavior of a dynamical system, typically with the purpose of regulating certain variables or of tracking desired signals. Often, either stability of the closed-loop system is an explicit requirement, or else the problem can be recast in a form that involves stabilization (e.g., of an error signal).
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The main objective of control is to modify the behavior of a dynamical system, typically with the purpose of regulating certain variables or of tracking desired signals. Often, either stability of the closed-loop system is an explicit requirement, or else the problem can be recast in a form that involves stabilization (e.g., of an error signal).
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Using Lyapunov Functions to Construct Lyapunov Functionals for Delay Differential Equations
SIAM Journal on Applied Dynamical Systems, 2015Given that a Lyapunov function is known for a particular system, we outline an approach for determining terms in the system that can be replaced by similar terms that include delay, without changing the global stability. The approach is based on adding integral terms to the original Lyapunov function so that the new Lyapunov derivative is still ...
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Nondecreasing Lyapunov functions
2014We propose the notion of nondecreasing Lyapunov functions which can be used to prove stability or other properties of the system in question. This notion is in particular useful in studying switched or hybrid systems. We illustrate the concept by a general construction of such a nondecreasing Lyapunov function for a class of planar hybrid systems.
Defoort, Michael +2 more
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Journal of the Society for Industrial and Applied Mathematics Series A Control, 1962
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SARS-CoV-2 variants, spike mutations and immune escape
Nature Reviews Microbiology, 2021William T Harvey +2 more
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