Results 271 to 280 of about 92,845 (311)

Lyapunov Functions and Cone Families

Journal of Statistical Physics, 2012
We describe systematically the relation between Lyapunov functions and nonvanishing Lyapunov exponents, both for maps and flows. This includes a brief survey of the existing results in the area. In particular, we consider separately the cases of nonpositive and arbitrary Lyapunov functions, thus yielding optimal criteria for negativity and positivity ...
Barreira, Luis, Dragičević, Davor, Valls, Claudia   +2 more
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Using Lyapunov Functions to Construct Lyapunov Functionals for Delay Differential Equations

SIAM Journal on Applied Dynamical Systems, 2015
Given 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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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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Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks

SIAM Journal on Control and Optimization, 2017
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Haitao Li 0001, Yuzhen Wang
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Higher Derivatives of Lyapunov Functions

Differential Equations, 2004
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A Lyapunov function proof of Poincare's theorem

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002
One of the most fundamental results in analysing the stability properties of periodic orbits and limit cycles of dynamical systems is Poincare's theorem. The proof of this result involves system analytic arguments along with the Hartman-Grobman theorem.
Wassim M. Haddad 0001, Sergey G. Nersesov, VijaySekhar Chellaboina   +2 more
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Semidefinite lyapunov functions stability and stabilization

Mathematics of Control, Signals, and Systems, 1996
The paper gives some weakening of the basic Lyapunov theorems by obtaining stability and asymptotic stability for nonnegatively definite Lyapunov functions. These results allow simpler proofs for some previously known results and some extension of the stabilization results for systems that are affine in the control.
Iggidr, Abderrahman, Kalitine, Boris, Outbib, Rachid   +2 more
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Applications of a family of lyapunov functions

Journal of Applied Mathematics and Mechanics, 2000
The author considers the perturbed motion equations in the form \[ \begin{aligned} &A_1(x_1,\dot x_1,x_2,t)\ddot x_1 = B_1(x_1,\dot x_1,x_2,t);\\ &N_1(x_1,\dot x_1,x_2,t)\ddot x_2 = K_1(x_1,\dot x_1,x_2,t), \end{aligned}\tag{1} \] where \(A_1\) and \(N_1\) are \((n\times n)\)- and \((m\times m)\)-matrices, \(x_1\) and \(B_1\) are \(n\)-dimensional ...
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The problem of constructing a lyapunov function

Journal of Applied Mathematics and Mechanics, 1985
An algorithm which, for a wide class of problems, enables a Lyapunov function with a negative-sign derivative to be reconstructed as a Lyapunov function with a negative-definite derivative, is proposed. This algorithm supplements the well-known method of reconstructing a Lyapunov function. Examples are considered.
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Vector Lyapunov Functions

Journal of the Society for Industrial and Applied Mathematics Series A Control, 1962
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