Results 281 to 290 of about 29,097,853 (357)

Computing Lyapunov exponents of continuous dynamical systems: method of Lyapunov vectors

Chaos, Solitons & Fractals, 2005
The paper proposes a new method for computing the Lyapunov characteristic exponents of general continuous dynamical systems. There are several methods for finding numerical values of Lyapunov's exponents, e.g., Wolf's algorithm and the QR method.
Lu, Jia, Yang, Guolai, Oh, Hyounkyun, Luo, Albert C. J.   +3 more
openaire   +1 more source

Some Refinements of Lyapunov's Second Method

Canadian Journal of Mathematics, 1965
Lyapunov's second method is a well-known and powerful tool for studying the behaviour of solutions of a system of differential equations. One approach to the theory is the comparison method developed by Corduneanu (4). This approach has the advantage that it also leads to other results on asymptotic behaviour which originally appeared to be unrelated ...
openaire   +1 more source

Adaptive optimized backstepping tracking control for full‐state constrained nonlinear strict‐feedback systems without using barrier Lyapunov function method

Optimal control applications & methods
In this article, the problem of adaptive optimal tracking control is studied for nonlinear strict‐feedback systems. While not directly measurable, the states of these systems are subject to both time‐varying and asymmetric constraints.
Boyan Zhu, Ning Xu, Guangdeng Zong, Xudong Zhao   +3 more
semanticscholar   +1 more source

Method of Lyapunov Functions

2020
The celebrated Lyapunov function method (or the direct Lyapunov method) introduced in the Ph.D. thesis of A. M. Lyapunov in 1892 is a simple effective tool for stability analysis of differential equations. The main advantage of this method lies in the fact that a decision on stability or instability can be made by means of a certain investigation of ...
openaire   +1 more source

Discontinuous Event-Triggered Control for Local Stabilization of Memristive Neural Networks With Actuator Saturation: Discrete- and Continuous-Time Lyapunov Methods

IEEE Transactions on Neural Networks and Learning Systems, 2021
Yingjie Fan, Xia Huang, Zhen Wang, Jianwei Xia, Hao Shen   +4 more
semanticscholar   +1 more source

Design of Interval Type-2 Fuzzy-Based Sampled-Data Controller for Nonlinear Systems Using Novel Fuzzy Lyapunov Functional and its Application to PMSM

IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018
This paper presents interval type-2 fuzzy-based sampled-data controller for nonlinear systems using novel fuzzy Lyapunov functional. To do this, a type-2 fuzzy model is adapted for the nonlinear systems and a type-2 fuzzy-based sampled-data controller is
Lakshmanan Shanmugam, Y. Joo
semanticscholar   +1 more source

The Lyapunov Function Method

1999
In Chapter 7 we discussed the first approach to realization of the Lyapunov direct method for FDE based on application of the Lyapunov functionals. In the second approach finite dimensional Lyapunov’s functions v(t, x): R × R n →R are used.
openaire   +1 more source

The Lyapunov–Razumikhin Method: CNNs

2013
In this chapter, by using the concept of differential equations with piecewise constant arguments of generalized type [13–15, 18], the model of cellular neural networks (CNNs) [79, 80] is developed. Lyapunov–Razumikhin technique is applied to find sufficient conditions for uniform asymptotic stability of equilibria.
Marat Akhmet, Enes Yılmaz
openaire   +1 more source

Lyapunov's direct method in stability theory (review)

International Applied Mechanics, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lakshmikantham, V., Martynyuk, A. A.
openaire   +2 more sources

Generalized energies and the Lyapunov method

1992
Thus far in convection studies we have explored uses of the energy method that have concentrated on employing some form of kinetic-like energy, involving combinations of L 2 integrals of perturbation quantities. While this is fine and yields strong results for a large class of problem, there are many situations where such an approach leads only to weak
openaire   +1 more source