Asymptotic comparison of the solutions of linear time-delay systems with point and distributed lags with those of their limiting equations.
Asymptotical convergence of the solutions of a linear differential equation with delays.
Behavior of the solutions to second order linear autonomous delay differential equations.
Boundary value problems for delay differential systems.
Characterization of shadowing for linear autonomous delay differential equations
A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.
Commutants of the Dunkl Operators in C(R)
2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80The Dunkl operators.* Supported by the Tunisian Research Foundation under 04/UR/15-02.
Construction of the general solution of planar linear discrete systems with constant coefficients and weak delay.
Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections
The problem of the decentralized robust tracking and model following is considered for a class of uncertain large scale systems including time-varying delays in the interconnections. On the basis of the Razumikhin-type theorem and the Lyapunov stability theory, a class of decentralized memoryless local state feedback controllers is proposed for robust tracking of dynamical signals. It is shown that by employing the proposed decentralized robust tracking controllers, one can guarantee that the tracking...
Delay-dependent stability of high-order neutral systems
In this note, we are concerned with delay-dependent stability of high-order delay systems of neutral type. A bound of unstable eigenvalues of the systems is derived by the spectral radius of a nonnegative matrix. The nonnegative matrix is related to the coefficient matrices. A stability criterion is presented which is a necessary and sufficient condition for the delay-dependent stability of the systems. Based on the criterion, a numerical algorithm is provided which avoids the computation of the...
Differential inequalities for one component of solution vector for systems of linear functional differential equations.
Estimates for Principal Lyapunov Exponents: A Survey
This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....
Exact solutions of a linear functional differential equation.
Exponential stability and estimation of solutions of linear differential systems of neutral type with constant coefficients.
Exponential stability criteria of linear non-autonomous systems with multiple delays.
Exponential stability of linear stochastic differential equations with bounded delay and the W-transform.
Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays
The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices of the system with delays satisfy algebraic matrix equations with coefficients of the characteristic polynomial.
Formulas of variation for a solution of neutral differential equations with continuous initial condition.
General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations
New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.
Hyers-Ulam stability of the delay equation .
Infinite systems of hyperbolic differential-functional inequalities.