نتایج جستجو برای: lyapunov theory

تعداد نتایج: 793532  

1999
J. Bolte B. Müller A. Schäfer

We investigate the relationship between the Lyapunov exponents of periodic trajectories, the average and fluctuations of Lyapunov exponents of ergodic trajectories, and the ergodic autocorrelation time for the two-dimensional hyperbola billiard. We then study the fluctuation properties of the ergodic Lyapunov spectrum of classical SU(2) gauge theory on a lattice. Our results are consistent with...

2015
HASSAN SAOUD

Semistability is the property whereby the solutions of a dynamical system converge to a Lyapunov stable equilibrium point determined by the system initial conditions. We extend the theory of semistability to a class of first-order evolution variational inequalities, and study the finite-time semistability. These results are Lyapunov-based and are obtained without any assumptions of sign definit...

2005
Stefan Weigert

We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperboli...

1998
James Hanssen Walter Wilcox

The dependence of the Lyapunov exponent on the closeness parameter, ǫ, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we develop theoretical expressions for an isolated tangency channel in which the Lyapunov exponent is defined on single channel passes. Numerical simulations were done to co...

2002

In Robust control design of nonlinear uncertain systems, stability theory plays an important role in engineering systems. For any given control system, it is crucial to have a stable system since an unstable control system is useless. Lyapunov . stability criterion is a general and useful procedure for studying the stability of nonlinear systems. The Lyapunov stability theory include two method...

2006
James Justus Mark Colyvan Greg Mikkelson Alexander Moffett Eric Pianka Mark Sainsbury

Ecologists have proposed several incompatible definitions of ecological stability. Emulating physicists, mathematical ecologists commonly define it as Lyapunov stability. This formalizes the problematic concept by integrating it into a well-developed mathematical theory. The formalization also seems to capture the intuition that ecological stability depends on how ecological systems respond to ...

2012
Sundarapandian Vaidyanathan

This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for thes...

2013
A. Bennassar A. Abbou M. Akherraz M. Barara

In this paper, we propose a sensorless backstepping control of induction motor (IM) associated with three levels neutral clamped (NPC) inverter. First, the backstepping approach is designed to steer the flux and speed variables to theirs references and to compensate the uncertainties. A Lyapunov theory is used and it demonstrates that the dynamic trajectories tracking are asymptotically stable....

Journal: :Applied Mathematics and Computer Science 2013
Tomasz Zubowicz Mietek A. Brdys

This paper addresses the problem of model-based global stability analysis of discrete-time Takagi–Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the c...

2003
Raúl O. Vallejos Celia Anteneodo

We calculate analytically the largest Lyapunov exponent of the so-called αXY Hamiltonian in the high energy regime. This system consists of a d-dimensional lattice of classical spins with interactions that decay with distance following a powerlaw, the range being adjustable. In disordered regimes the Lyapunov exponent can be easily estimated by means of the “stochastic approach”, a theoretical ...

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