Results 191 to 200 of about 9,796 (225)

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
openaire   +1 more source

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
openaire   +3 more sources

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 ...
openaire   +2 more sources

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.
openaire   +1 more source

Lyapunov functionals for linear continuous-time difference systems: A single delay case

Systems and Control Letters, 2023
Daniel Melchor-Aguilar
exaly  

Vector Lyapunov Functions

Journal of the Society for Industrial and Applied Mathematics Series A Control, 1962
openaire   +1 more source

Approximations of Lyapunov functionals for ISS analysis of a class of higher dimensional nonlinear parabolic PDEs

Automatica, 2021
Jun Zheng, Guchuan Zhu
exaly  

Lyapunov functions

2023
openaire   +1 more source

On the construction of Lyapunov functions. I

The author studies vector fields on finite-dimensional smooth manifolds. To construct a Lyapunov function related to an equilibrium of a vector field, he uses the concept of `pilot function' introduced by him in [Autom. Remote Control 61, No. 4, Part 1, 585--594 (2000); translation from Avtom. Telemekh. 2000, No. 4, 51--60 (2000; Zbl 1060.34505)].
openaire   +2 more sources

Stability Analysis of Neural Networks With Time-Varying Delay by Constructing Novel Lyapunov Functionals

IEEE Transactions on Neural Networks and Learning Systems, 2018
Tae H Lee, Hieu Trinh, Ju H Park
exaly