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Showing 1 to 20 of 373 for “"Lyapunov"”.
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Almost Lyapunov functions
… dynamical system that verifies the classical Lyapunov criterion is globally asymptotically stable for the case when the Lyapunov function is strictly decreasing along the solution. We define an almost Lyapunov function to be a candidate Lyapunov function whose derivative with respect to time …
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Lyapunov Exponents, Entropy and Dimension
We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a …
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A Lyapunov analysis of LRU
… (TTL) cache. In this thesis, we present a unique Lyapunov based proof for an asymptotically exact TTL approximation for the steady state distribution of our LRU Markov model. We further present ongoing theoretical extensions to other variants of LRU, as well as simulations that validate our model. …
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ON THE LYAPUNOV-TYPE DIAGONAL STABILITY
In this dissertation we study the Lyapunov diagonal stability and its extensions through partitions of the index set {1,...,n}. This type of matrix stability plays an important role in various applied areas such as population dynamics, systems theory and complex networks. We first examine a result …
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Nonlinear control with two complementary Lyapunov function
If a Lyapunov function is known, a dynamic system can be stabilized. However, computing or selecting a Lyapunov function is often challenging. This dissertation presents a new approach which eliminates this challenge: a simple control Lyapunov function [CLF] is assumed then the algorithm seeks to …
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Computation of Lyapunov functions and stability of interconnected systems
… we investigate the problems of computation of Lyapunov functions and stability analysis of interconnected systems. In Chapter 1, preliminary results about stability, definitions of Lyapunov functions and triangulations are presented. In order to analyse stability of interconnected systems in …
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Lyapunov-type inequality and eigenvalue estimates for fractional problems
<p>In this work, we establish the Lyapunov-type inequalities for the fractional boundary value problems with Hilfer derivative for different boundary conditions. We apply this inequality to fractional eigenvalue problems and prove one of the important results of real zeros of certain Mittag-Leffler …
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Quantifying Dynamic Stability of Musculoskeletal Systems using Lyapunov Exponents
Increased attention has been paid in recent years to the means in which the body maintains stability and the subtleties of the neurocontroller. Variability of kinematic data has been used as a measure of stability but these analyses are not appropriate for quantifying stability of dynamic systems. …
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Computation of Lyapunov Exponents and Control of a Hyperchaotic System
… Chen system and also estimates the largest Lyapunov characteristic exponent (LCE) and provides a method to compute the entire Lyapunov spectrum of the dynamical system. The computation of the Lyapunov spectrum relies on calculating the order-p LCEs and repeated application of the …
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A Lyapunov-based small-gain theorem for interconnected switched systems
… defined to enable the construction of hybrid ISS Lyapunov functions. Apart from justifying the ISS property of their corresponding switched systems, these hybrid ISS Lyapunov functions are then combined to establish a Lyapunov-type small-gain condition which guarantees that the interconnected …
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Investigating Hamiltonian dynamics by the method of covariant Lyapunov vectors
In this thesis, we review the theory of Lyapunov exponents and covariant Lyapunov vectors (CLVs) and use these objects to numerically investigate the dynamics of several autonomous Hamiltonian systems. The algorithm which we use for computing CLVs is the one developed by Ginelli and collaborators …
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Energy level statistics and Lyapunov exponent in the stadium billiard
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Physics, 1995.
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Lyapunov-Based Robust and Adaptive Control Design for nonlinear Uncertain Systems
… asymptotically stabilize the system via both a Lyapunov-based stability proof and numerical simulation results.
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Statistical properties and scaling of the Lyapunov exponents in stochastic systems
… mit einer stochastischen Theorie für die Lyapunov-Exponenten befaßt sind. Mit Hilfe dieser Theorie werden universelle Skalengesetze untersucht, die in gekoppelten chaotischen und ungeordneten Systemen auftreten. Zunächst werden zwei zeitkontinuierliche stochastische Modelle für schwach …
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Algebraic relaxations and hardness results in polynomial optimization and Lyapunov analysis
… on existence of polynomial and sum of squares Lyapunov functions. We present a globally asymptotically stable polynomial vector field with no polynomial Lyapunov function. We show via an explicit counterexample that if the degree of the polynomial Lyapunov function is fixed, then sos …
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Biodynamic Analysis of Human Torso Stability using Finite Time Lyapunov Exponents
… First, the time series averaged finite time Lyapunov exponent is calculated from data obtained during seated stability experiments. The Lyapunov exponent is found to increase with increasing task difficulty. Second, a new metric for evaluating torso stability is introduced, the threshold of …
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Robust stabilization of linear time-invariant uncertain systems via Lyapunov theory
… is an n x n matrix and B̅(γ) is an n x m matrix. Lyapunov theory is exploited to establish the conditions for stabilizability of the closed loop system. We consider a Lyapunov function with an uncertain symmetric positive definite matrix P. The uncertain matrix P satisfies the Lyapunov equation …
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The analysis and control of nonlinear systems using Lyapunov stability theory
Techniques based on Lyapunov theory for the stability analysis and control of nonlinear systems are developed. In the first part of this work, procedures for determining conditions of guaranteed asymptotic stability are developed for nonlinear, uncontrolled systems. A second order model of an …
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