Results 211 to 220 of about 7,527 (244)

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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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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A Fuzzy Lyapunov Function Method to Stability Analysis of Fractional-Order T–S Fuzzy Systems

IEEE Transactions on Fuzzy Systems, 2022
Zhanshan Wang, Xiaofei Fan
exaly  

Vector Lyapunov Functions

Journal of the Society for Industrial and Applied Mathematics Series A Control, 1962
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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)].
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Neural Networks Based Lyapunov Functions for Transient Stability Analysis and Assessment of Power Systems

IEEE Transactions on Industry Applications, 2023
Tong Wang, Xiaotong Wang
exaly  

A Multiple Lyapunov Function Approach to Stabilization of Fuzzy Control Systems

IEEE Transactions on Fuzzy Systems, 2003
Kazuo Tanaka, H O Wang
exaly  

Lyapunov Functions

1987
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On Constructing Lyapunov Functions for Multi-Agent Systems

Automatica, 2015
Zhihua Qu, Hongwei Zhang, Li Zhongkui
exaly