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Structured and simultaneous Lyapunov functions for system stability problems
Lyapunov function system robustness quadratic lyapunov function the numerical values
2015/8/13
It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of dx/dt...
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...
Constructing Lyapunov Functions for Nonlinear Delay-Differential Equations using Semidefinite Programming
Delay-Differential Equations Lyapunov Functions
2015/6/19
The search for a polynomial Lyapunov function proving delay-independent stability of multivariate nonlinear polynomial delay differential equations is approached using semidefinite programming. The fu...
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...
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...