Results 201 to 210 of about 7,504,828 (242)

Lyapunov Stability Theory

2014
Basic concepts for the Lyapunov stability are introduced. Conditions are obtained for the stability of linear equations with constant, periodic, and general variable coefficients. Linearization and Lyapunov functions are used to deal with nonlinear stability problems.
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A. M. Lyapunov's stability theory—100 years on

IMA Journal of Mathematical Control and Information, 1992
Summary: On 12 October 1892 (according to the modern calendar) Alexandr Mikhailovich Lyapunov defended his doctoral thesis `The general problem of the stability of motion' at Moscow University. A brief history of Lyapunov's life and tragic death is given, and followed by a section highlighting the important ideas in his thesis of 1892.
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Lyapunov Stability Theory

2018
Stability of nonlinear systems are discussed in this chapter. Lyapunov stability, asymptotic stability, and exponential stability of an equilibrium point of a nonlinear system are defined. The Lyapunov’s direct method is introduced as an indispensable tool for analyzing stability of nonlinear systems.
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Stability theory and Lyapunov's second method

Archive for Rational Mechanics and Analysis, 1963
1. Introduct ion In two papers appearing in t949 and t956, MASSERA [8, 9] made a number of significant advances in LYAPUNOV'S second method and the theory of stability of ordinary differential equations. He extended the work of LYAPUNOV [31, MALKIN [4--71 and others and arrived at both necessary and sufficient conditions for stability in terms of a ...
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On the Stability of Pointer States Using Lyapunov Theory

IFAC Proceedings Volumes, 2012
Abstract Pointer states are states of an open quantum system that are able to survive the constant monitoring of the system by an environment. It has been shown that open systems that are prepared in superpositions of such pointer states quickly decohere and evolve into classical statistical mixtures of (pure) pointer states.
Ram Somaraju, Ian R. Petersen, Hugo Thienpont   +2 more
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Deep Lyapunov Learning: Embedding the Lyapunov Stability Theory in Interpretable Neural Networks for Transient Stability Assessment

IEEE Transactions on Power Systems
Tao Ding, Rudai Yan
exaly   +2 more sources

Investigation of human-robot interaction stability using Lyapunov theory

2008 IEEE International Conference on Robotics and Automation, 2008
For human-robot cooperation in the context of human-augmentation tasks, the stability of the control model is of great concern due to the risk for the human safety represented by a powerful robot. This paper investigates stability conditions for impedance control in this cooperative context and where touch is used as the sense of interaction.
Vincent Duchaine, Clément M. Gosselin
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Lyapunov’s theory methods in stability problems of singular systems

Nonlinear Analysis: Theory, Methods & Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On application of the Lyapunov matrix-functions in the theory of stability

Nonlinear Analysis: Theory, Methods & Applications, 1985
We consider the differential equation (1) \(\dot x=f(x)\), \(f(0)=0\) where \(x\in R^ n\), \(f\in C(R_+\times R^ n)\). Suppose that the solution \(\chi (t;x_ 0)\) of system (1) is unique and exists for all \(t\geq 0\) for \(t_ 0\geq 0\), \(x_ 0\in int N\), \(N\subseteq R^ n\), \(\chi (t_ 0,x_ 0)=x_ 0\).
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Elements of Lyapunov stability theory for dynamic equations on time scale

International Applied Mechanics, 2007
Stability of dynamic equations on time scale is analyzed. The main results are new conditions of stability, uniform stability, and uniform asymptotic stability for quasilinear and nonlinear ...
Bohner, M., Martynyuk, A. A.
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