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A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
Nonlinear systems quadratic lyapunov function and convex programming function
2015/8/12
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
A class of Lyapunov functionals for analyzing hybrid dynamical systems
Lyapunov functionals the hybrid system function hysteresis nonlinear system lyapunov functionals
2015/8/11
In this paper, we introduce a new class of Lyapunov functionals for analyzing hybrid dynamical systems. This class can be thought of as a generalization of the Lyapunov functional introduced by Yakubo...
Fast evaluation of quadratic control-Lyapunov policy
Quadratic lyapunov function quadratic programming the solution and optimization method computationally intensive control application
2015/8/7
The evaluation of a control-Lyapunov policy, with quadratic Lyapunov function, requires the solution of a quadratic program (QP) at each time step. For small problems this QP can be solved explicitly;...
Principal Lyapunov Exp onent and Principal Flo quet Bundle of Sto chas tic/Ra ndom Para b olic Equations
Principal Lyapunov Exp onen Principal Flo quet Bundle
2015/4/3
Problem – Extension of Principal Eigenvalue/Principal
Eigenfunction Theory for Time Independent Parabolic
Equations to Random Parabolic Equations
I Principal Eigenvalue/Principal Eigenfunction Theo...
Lyapunov Exponents for Infinite Dimensional Random Dynamical Systems in a Banach Space
Random Dynamical Systems Lyapunov Exponents
2015/4/3
Metric Dynamical System
Let be a probability space.
Let be a metric dynamical system:
(i)
(ii)
(iii) preserves th...
The Kullback-Liebler Divergence as a Lyapunov Function for Incentive Based Game Dynamics
The Kullback-Liebler Divergence Lyapunov Function Incentive Game Dynamics Dynamical Systems
2012/7/9
It has been shown that the Kullback-Leibler divergence is a Lyapunov function for the replicator equations at evolutionary stable states, or ESS. In this paper we extend the result to a more general c...
Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Multifractal analysis of some multiple ergodic averages non-constant Lyapunov exponents Dynamical Systems
2012/6/27
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
Entropy, Lyapunov exponents and the volume growth of boundary distortion under the action of dynamical systems
Lyapunov exponents the volume growth of boundary distortion the action of dynamical systems
2012/4/17
We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.
Morse decomposition and Lyapunov functions for dynamical systems
Differential equation and dynamical system Morse decomposition Lyapunov function
2011/10/18
In this paper, we review Morse decomposition and Lyapunov functions. Most of the results are due to Conley and are known. Attractor-repeller pairs and Morse decompositions are very useful to study the...
Existence of complete Lyapunov functions for semiflows on separable metric spaces
Lyapunov functions Semiflows Separable metric space
2011/9/23
Abstract: The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the exis...
Positive recurrence of piecewise Ornstein-Uhlenbeck processes and common quadratic Lyapunov functions
stability common quadratic Lyapunov function Lyapunov function piecewise OU process multi-server queues customer abandonment
2011/9/8
Abstract: We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion...
Entropy, Lyapunov Exponents and Escape Rates in Open Systems
Lyapunov Exponents Escape Rates Open Systems Dynamical Systems
2011/9/5
Abstract: We study the relation between escape rates and pressure in general dynamical systems with holes, where pressure is defined to be the difference between entropy and the sum of positive Lyapun...
Coordinate-invariant incremental Lyapunov functions
Coordinate-invariant incremental Lyapunov functions Optimization and Control
2011/9/6
Abstract: The notion of incremental stability was proposed by several researchers as a strong property of dynamical and control systems. In this type of stability, the focus is on the convergence of t...
Absolute continuity, Interpolation and the Lyapunov order
Nevanlinna-Pick interpolation representations Hardy algebra absolute continuity Lyapunov order
2011/8/24
Abstract: We extend our Nevanlinna-Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the boundaries of their discs of representati...
Local Gram-Schmidt and Covariant Lyapunov Vectors and Exponents for Three Harmonic Oscillator Problems
Lyapunov Instability Covariant Lyapunov Spectrum Gram-Schmidt Orthonormalization
2011/7/6
We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three
time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions re-
spectively....