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The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…

Analysis of PDEs · Mathematics 2023-12-21 Christoph Walker

We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the…

Optimization and Control · Mathematics 2024-10-30 Guang-Da Hu

This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…

Dynamical Systems · Mathematics 2025-10-30 Yacine Chitour , Felipe Gonçalves Netto , Guilherme Mazanti

The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…

Systems and Control · Electrical Eng. & Systems 2022-08-12 Francesco Ferrante , Giorgio Valmorbida

We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…

Numerical Analysis · Mathematics 2020-11-03 Wim Michiels , Luca Fenzi

This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the…

Systems and Control · Computer Science 2019-03-01 Yohei Hosoe , Tomomichi Hagiwara

Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…

Systems and Control · Computer Science 2015-09-07 Kwang-Ki K. Kim , Richard D. Braatz

In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the…

Dynamical Systems · Mathematics 2012-01-04 Ferenc Hartung

The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…

Dynamical Systems · Mathematics 2015-07-13 S. Sarif Hassan

The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…

Dynamical Systems · Mathematics 2020-05-13 Phi Ha

This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…

Dynamical Systems · Mathematics 2007-05-23 Ping Wei , Qiang Guan , Wensheng Yu , Long Wang

Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…

Optimization and Control · Mathematics 2012-09-11 Nikolaos Bekiaris-Liberis , Miroslav Krstic

In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…

Probability · Mathematics 2013-10-10 John A. D. Appleby , Jian Cheng , Alexandra Rodkina

We consider state-dependent delay equations (SDDE) obtained by adding delays to a planar ordinary differential equation with a limit cycle. These situations appear in models of several physical processes, where small delay effects are…

Dynamical Systems · Mathematics 2021-08-13 Jiaqi Yang , Joan Gimeno , Rafael de la Llave

Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…

Optimization and Control · Mathematics 2007-05-23 Eugenii Shustin , Emilia Fridman

We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…

Numerical Analysis · Mathematics 2019-05-22 Felipe Cucker , Teresa Krick

A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…

Probability · Mathematics 2018-10-25 Leonid Shaikhet

It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…

Optimization and Control · Mathematics 2017-03-02 Corentin Briat

An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations…

Systems and Control · Electrical Eng. & Systems 2020-03-26 Wim Michiels , Suat Gumussoy

In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…

Optimization and Control · Mathematics 2016-03-28 Evgeny Meyer , Matthew M. Peet