Related papers: Exponential stability of linear periodic differenc…
We study the asymptotic behavior of the solutions of the time-delayed higher-order dispersive nonlinear differential equation \begin{equation*} u_t(x,t)+Au(x,t) +\lambda_0(x) u(x,t)+\lambda(x) u(x,t-\tau )=0 \end{equation*} where…
Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with…
We explore the Hyers-Ulam stability of perturbations for a homogeneous linear differential system with $2\times 2$ constant coefficient matrix. New necessary and sufficient conditions for the linear system to be Hyers-Ulam stable are…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many such problems, the dominant…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
The Bohl-Perron result on exponential dichotomy for a linear difference equation $$ x(n+1)-x(n) + \sum_{l=1}^m a_l(n)x(h_l(n))=0, h_l(n)\leq n, $$ states (under some natural conditions) that if all solutions of the non-homogeneous equation…
We analyse the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. It is well-known that the existence of a positive {\tau} for which the corresponding discrete time…
In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…
We investigate a scalar characteristic exponential polynomial with complex coefficients associated with a first order scalar differential-difference equation. Our analysis provides necessary and sufficient conditions for allocation of the…
In the present paper, the exponential stability of the mono-tubular heat exchanger equation with boundary observation possessing a time delay and inner control is investigated through a simply proportional feedback. Firstly, the close-loop…
We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservation laws, as arises in modern biomorphology models, binary…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
PDEs with periodic boundary conditions are frequently used to model processes in large spatial environments, assuming solutions to extend periodically beyond some bounded interval. However, solutions to these PDEs often do not converge to a…
In this thesis we consider so-called linear evolutionary problems, a class of linear partial differential equations covering classical elliptic, parabolic and hyperbolic equations from mathematical physics as well as classes of…
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way…