相关论文: What ODE-Approximation Schemes of Time-Delay Syste…

Delay differential equations (DDEs) are infinite-dimensional systems, so even a scalar, unforced nonlinear DDE can exhibit chaos. Lyapunov exponents are indicators of chaos and can be computed by comparing the evolution of infinitesimally…

Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…

We review the Lyapunov functional method for linear ODEs and give an explicit construction of such functionals that yields sharp decay estimates, including an extension to defective ODE systems. As an application, we consider three…

This work is dedicated to the stability analysis of time-delay systems with a single constant delay using the Lyapunov-Krasovskii theorem. This approach has been widely used in the literature and numerous sufficient conditions of stability…

In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay…

This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…

We present a Chebyshev collocation method for linear ODE and DDE problems. We first give a posteriori estimates for the accuracy of the approximate solution of a scalar ODE initial value problem. Examples of the success of the estimate are…

Pointwise-in-time stability notions for Ordinary Differential Equations (ODEs) provide quantitative metrics for system performance by establishing bounds on the rate of decay of the system state in terms of initial condition -- allowing…

The focus of this work is on local stability of a class of nonlinear ordinary differential equations (ODE) that describe limits of empirical measures associated with finite-state weakly interacting N-particle systems. Local Lyapunov…

We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…

A new necessary and sufficient stability test in a tractable number of operations for linear neutral-type delay systems is introduced. It is developed in the Lyapunov-Krasovskii framework via functionals with prescribed derivatives. The…

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

In this contribution, we study an homogeneous class of nonlinear time delay systems with time-varying perturbations. Using the Lyapunov-Krasovskii approach, we introduce a functional that leads to perturbation conditions matching those…

This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The…

Many dynamical systems described by nonlinear ODEs are unstable. Their associated solutions do not converge towards an equilibrium point, but rather converge towards some invariant subset of the state space called an attractor set. For a…

Approximation theory for Lyapunov and Sacker-Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent, linear, ordinary differential equation (ODE) initial value problem in terms…

We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering.…

Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…

We consider the Goldstein-Taylor model, which is a 2-velocity BGK model, and construct the "optimal" Lyapunov functional to quantify the convergence to the unique normalized steady state. The Lyapunov functional is optimal in the sense that…