The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Luis F C Alberto - One of the best experts on this subject based on the ideXlab platform.
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an Invariance Principle for nonlinear discrete autonomous dynamical systems
IEEE Transactions on Automatic Control, 2007Co-Authors: Luis F C Alberto, T R Calliero, A C P MartinsAbstract:This note proposes an extension of LaSalle's Invariance Principle for nonlinear discrete autonomous dynamical systems. The Invariance Principle is extended to allow the first difference of the auxiliar scalar function (usually a Lyapunov function) to be positive in some bounded regions. Moreover, a uniform version is proposed to deal with nonlinear discrete dynamical systems that vary with parameters. Both extensions have the original Invariance Principle as a particular case. As a consequence, a larger class of systems can be treated with this new theory. The extensions are very useful to obtain attractor estimates as well as their corresponding stability regions. The uniform version, in particular, is useful to obtain estimates that are uniform regarding parameters
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lyapunov function for power systems with transfer conductances extension of the Invariance Principle
2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491), 2003Co-Authors: N G Bretas, Luis F C AlbertoAbstract:Summary form only given. In many engineering and physical problems, it is very difficult to find a Lyapunov function satisfying the classical version of the LaSalle's Invariance Principle. This difficulty has been a big drawback in the application of energetic methods to stability analysis of power systems with more realistic models. In this work, an extension of the Invariance Principle is used to support the proposal of a new function, which is an extended Lyapunov function for power systems incorporating the transfer conductances. This function was tested in a single-machine-infinite-bus system and also in some multimachine systems. The results show that the proposed function can be used to obtain good estimates of the critical clearing time.
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lyapunov function for power systems with transfer conductances extension of the Invariance Principle
IEEE Transactions on Power Systems, 2003Co-Authors: N G Bretas, Luis F C AlbertoAbstract:In many engineering and physical problems, it is very difficult to find a Lyapunov Function satisfying the classical version of the LaSalle's Invariance Principle. This difficulty has been a big drawback in the application of energetic methods to stability analysis of power systems with more realistic models. In this work, an extension of the Invariance Principle is used to support the proposal of a new function which is an extended Lyapunov function for power systems incorporating the transfer conductances. This function was tested in a single-machine-infinite-bus system and also in some multimachine systems. The results show that the proposed function can be used to obtain good estimates of the critical clearing time.
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uniform Invariance Principle and synchronization robustness with respect to parameter variation
Journal of Differential Equations, 2001Co-Authors: Hildebrando M Rodrigues, Luis F C Alberto, N G BretasAbstract:Abstract The objective of this work is to obtain uniform estimates, with respect to parameters, of the attractor and of the basin of attraction of a dynamical system and to apply these results to analyze the roughness of the synchronization of two subsystems. These estimates are obtained through a uniform version of the Invariance Principle of La Salle which is stated and proved in this work.
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uniform Invariance Principle and synchronization robustness with respect to parameter variation
Conference on Decision and Control, 2000Co-Authors: N G Bretas, Luis F C AlbertoAbstract:The object of this work is to obtain uniform estimates, with respect to parameters, of the attractor and of the basin of attraction of a dynamical system and to apply these results to analyze the roughness of the synchronization of two subsystems. These estimates are obtained through an uniform version of the Invariance Principle of La Salle which is stated and proved in this work.
Artur Avila - One of the best experts on this subject based on the ideXlab platform.
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extremal lyapunov exponents an Invariance Principle and applications
Inventiones Mathematicae, 2010Co-Authors: Artur Avila, Marcelo VianaAbstract:We propose a new approach to analyzing dynamical systems that combine hyperbolic and non-hyperbolic (“center”) behavior, e.g. partially hyperbolic diffeomorphisms. A number of applications illustrate its power. We find that any ergodic automorphism of the 4-torus with two eigenvalues in the unit circle is stably Bernoulli among symplectic maps. Indeed, any nearby symplectic map has no zero Lyapunov exponents, unless it is volume preserving conjugate to the automorphism itself. Another main application is to accessible skew-product maps preserving area on the fibers. We prove, in particular, that if the genus of the fiber is at least 2 then the Lyapunov exponents must be different from zero and vary continuously with the map. These, and other dynamical conclusions, originate from a general Invariance Principle we prove in here. It is formulated in terms of smooth cocycles, that is, fiber bundle morphisms acting by diffeomorphisms on the fibers. The extremal Lyapunov exponents measure the smallest and largest exponential rates of growth of the derivative along the fibers. The Invariance Principle states that if these two numbers coincide then the fibers carry some amount of structure which is transversely invariant, that is, invariant under certain canonical families of homeomorphisms between fibers.
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extremal lyapunov exponents an Invariance Principle and applications
Inventiones Mathematicae, 2010Co-Authors: Artur Avila, Marcelo VianaAbstract:We propose a new approach to analyzing dynamical systems that combine hyperbolic and non-hyperbolic (“center”) behavior, e.g. partially hyperbolic diffeomorphisms. A number of applications illustrate its power.
Florence Merlevède - One of the best experts on this subject based on the ideXlab platform.
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almost sure Invariance Principle for the kantorovich distance between the empirical and the marginal distributions of strong mixing sequences
Statistics & Probability Letters, 2021Co-Authors: Jérôme Dedecker, Florence MerlevèdeAbstract:Abstract We prove a strong Invariance Principle for the Kantorovich distance between the empirical distribution and the marginal distribution of stationary α -mixing sequences.
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Rates in the strong Invariance Principle for ergodic automorphisms of the torus
Stochastics and Dynamics, 2014Co-Authors: Jérôme Dedecker, Florence Merlevède, Françoise PeneAbstract:Let T be an ergodic automorphism of the d-dimensional torus. In the spirit of Le Borgne, we give conditions on the Fourier coeffi cients of a real valued function f under which the Birkhoff sums satis fy a strong Invariance Principle. Next, reinforcing the condition on the Fourier coeffi cients in a natural way, we obtain explicit rates of convergence in the strong Invariance Principle.
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rates in the strong Invariance Principle for ergodic automorphisms of the torus
Stochastics and Dynamics, 2014Co-Authors: Jérôme Dedecker, Florence Merlevède, Françoise PeneAbstract:Let T be an ergodic automorphism of the d-dimensional torus 𝕋d. In the spirit of Le Borgne, we give conditions on the Fourier coefficients of a function f from 𝕋d to ℝ under which the partial sums f ◦ T + f ◦ T2 + ⋯ + f ◦ Tn satisfy a strong Invariance Principle. Next, reinforcing the condition on the Fourier coefficients in a natural way, we obtain explicit rates of convergence in the strong Invariance Principle, up to n1/4log n.
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On martingale approximations and the quenched weak Invariance Principle
2012Co-Authors: Christophe Cuny, Florence MerlevèdeAbstract:In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in $\h$ (a real and separable Hilbert space) admits an approximation, in $\LL^p (\h) $, $p>1$, by a martingale with stationary differences and we then estimate the error of approximation in $\LL^p (\h) $. The results are exploited to further investigate the behavior of the partial sums. In particular we obtain new projective conditions concerning the Marcinkiewicz-Zygmund theorem, the moderate deviations Principle and the rates in the central limit theorem in terms of Wasserstein distances. The conditions are well suited for a large variety of examples including linear processes or various kinds of weak dependent or mixing processes. In addition, our approach suits well to investigate the quenched central limit theorem and its Invariance Principle via martingale approximation, and allows us to show that they hold under the so-called Maxwell-Woodroofe condition that is known to be optimal.
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Rates of convergence in the strong Invariance Principle under projective criteria
Electronic Journal of Probability, 2012Co-Authors: Jérôme Dedecker, Paul Doukhan, Florence MerlevèdeAbstract:We give rates of convergence in the strong Invariance Principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples. We present some applications to a reversible Markov chain, to symmetric random walks on the circle, and to functions of dependent sequences.
Ofer Zeitouni - One of the best experts on this subject based on the ideXlab platform.
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quenched Invariance Principle for random walks in balanced random environment
Probability Theory and Related Fields, 2012Co-Authors: Xiaoqin Guo, Ofer ZeitouniAbstract:We consider random walks in a balanced random environment in $${\mathbb{Z}^d}$$ , d ≥ 2. We first prove an Invariance Principle (for d ≥ 2) and the transience of the random walks when d ≥ 3 (recurrence when d = 2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.
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quenched Invariance Principle for random walks in balanced random environment
arXiv: Probability, 2010Co-Authors: Xiaoqin Guo, Ofer ZeitouniAbstract:We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an Invariance Principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.
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a quenched Invariance Principle for certain ballistic random walks in i i d environments
arXiv: Probability, 2008Co-Authors: Noam Berger, Ofer ZeitouniAbstract:We prove that every random walk in i.i.d. environment in dimension greater than or equal to 2 that has an almost sure positive speed in a certain direction, an annealed Invariance Principle and some mild integrability condition for regeneration times also satisfies a quenched Invariance Principle. The argument is based on intersection estimates and a theorem of Bolthausen and Sznitman.
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An Invariance Principle for isotropic diffusions in random environment
Inventiones mathematicae, 2006Co-Authors: Alain-sol Sznitman, Ofer ZeitouniAbstract:We investigate in this work the asymptotic behavior of isotropic diffusions in random environment that are small perturbations of Brownian motion. When the space dimension is three or more, we prove an Invariance Principle as well as transience. Our methods also apply to questions of homogenization in random media.
N G Bretas - One of the best experts on this subject based on the ideXlab platform.
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lyapunov function for power systems with transfer conductances extension of the Invariance Principle
2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491), 2003Co-Authors: N G Bretas, Luis F C AlbertoAbstract:Summary form only given. In many engineering and physical problems, it is very difficult to find a Lyapunov function satisfying the classical version of the LaSalle's Invariance Principle. This difficulty has been a big drawback in the application of energetic methods to stability analysis of power systems with more realistic models. In this work, an extension of the Invariance Principle is used to support the proposal of a new function, which is an extended Lyapunov function for power systems incorporating the transfer conductances. This function was tested in a single-machine-infinite-bus system and also in some multimachine systems. The results show that the proposed function can be used to obtain good estimates of the critical clearing time.
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lyapunov function for power systems with transfer conductances extension of the Invariance Principle
IEEE Transactions on Power Systems, 2003Co-Authors: N G Bretas, Luis F C AlbertoAbstract:In many engineering and physical problems, it is very difficult to find a Lyapunov Function satisfying the classical version of the LaSalle's Invariance Principle. This difficulty has been a big drawback in the application of energetic methods to stability analysis of power systems with more realistic models. In this work, an extension of the Invariance Principle is used to support the proposal of a new function which is an extended Lyapunov function for power systems incorporating the transfer conductances. This function was tested in a single-machine-infinite-bus system and also in some multimachine systems. The results show that the proposed function can be used to obtain good estimates of the critical clearing time.
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uniform Invariance Principle and synchronization robustness with respect to parameter variation
Journal of Differential Equations, 2001Co-Authors: Hildebrando M Rodrigues, Luis F C Alberto, N G BretasAbstract:Abstract The objective of this work is to obtain uniform estimates, with respect to parameters, of the attractor and of the basin of attraction of a dynamical system and to apply these results to analyze the roughness of the synchronization of two subsystems. These estimates are obtained through a uniform version of the Invariance Principle of La Salle which is stated and proved in this work.
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uniform Invariance Principle and synchronization robustness with respect to parameter variation
Conference on Decision and Control, 2000Co-Authors: N G Bretas, Luis F C AlbertoAbstract:The object of this work is to obtain uniform estimates, with respect to parameters, of the attractor and of the basin of attraction of a dynamical system and to apply these results to analyze the roughness of the synchronization of two subsystems. These estimates are obtained through an uniform version of the Invariance Principle of La Salle which is stated and proved in this work.
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on the Invariance Principle generalizations and applications to synchronization
IEEE Transactions on Circuits and Systems, 2000Co-Authors: Hildebrando M Rodrigues, Luis F C Alberto, N G BretasAbstract:In many engineering and physics problems it is very hard to find a Lyapunov function satisfying the classical version of the LaSalle's Invariance Principle. In this work, an extension of the Invariance Principle, which includes cases where the derivative of the Lyapunov function along the solutions is positive on a bounded set, is given. As a consequence, a larger class of problems may now be considered. The results are used to obtain estimates of attractors which are independent of coupling parameters. They are also applied to study the synchronization of coupled systems, such as coupled power systems and coupled Lorenz systems. Estimates on the coupling term are obtained in order to accomplish the synchronization.
