相关论文: A Lyapunov and Sacker-Sell spectral stability theo…
We generalize the theory of underlying one-step methods to strictly stable general linear methods (GLMs) solving nonautonomous ordinary differential equations (ODEs) that satisfy a global Lipschitz condition. We combine this theory with the…
The article proposes an approach to complete-type and related Lyapunov-Krasovskii functionals that neither requires knowledge of the delay-Lyapunov matrix function nor does it involve linear matrix inequalities. The approach is based on…
This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…
A scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed. This scheme leads to the same limiting differential equation as the original scheme and therefore has the same…
The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization…
The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nystr\"om (RKN) methods with varying step sizes is investigated. It is shown that when linear constant coefficient…
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…
We present the stability and error analysis of the unified Petrov-Galerkin spectral method, developed in \cite{samiee2017Unified}, for linear fractional partial differential equations with two-sided derivatives and constant coefficients in…
We present a straightforward and reliable continuous method for computing the full or a partial Lyapunov spectrum associated with a dynamical system specified by a set of differential equations. We do this by introducing a stability…
In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…
Under the condition of nonuniformly bounded growth, %nonuniform exponential dichotomy spectrum for nonautonomous linear system is proposed the relationship of the nonuniform exponential dichotomy spectrum and the other two classical…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
For the ordinary differential equation (ODE) $\dot{x}(t) = f(t,x)$, $x(0) = x_0$, $t\geq 0$, $x\in R^d$, assume $f$ to be at least continuous in $t$ and locally Lipshitz in $x$, and if necessary, several times continuously differentiable in…
In this paper we study application of Le Cam's one-step method to parameter estimation in ordinary differential equations models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular…
Stability analysis tools are essential to understanding and controlling any engineering system. Recently sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different timescales appear. The singular perturbation method…