Systems Of Linear Functional Differential Equations Research Articles

Comparison Theorems from the Theory of Monotone Dynamical Systems for Linear Systems of Functional-Differential Equations with Linearly Transformed Argument

Comparison Theorems from the Theory of Monotone Dynamical Systems for Linear Systems of Functional-Differential Equations with Linearly Transformed Argument

Asymptotic Limits of the Solutions of Linear Systems of Functional-Differential Equations with Linear and Constant Delays

Asymptotic Limits of the Solutions of Linear Systems of Functional-Differential Equations with Linear and Constant Delays

Lyapunov’s direct method for linear systems of functional-differential equations in Sobolev space

We establish a criterion for exponential stability in the H1-topology in terms of operator inequalities for a linear FDE system of retarded type by Lyapunov’s direct method. As a corollary, some sufficient condition of exponential stability in terms of the matrix specifying the Stieltjes integral is obtained in the autonomous case. A few examples illustrating the results are exhibited.

A class of controls for a functional-differential continuous-discrete system

We consider control problems for linear systems of functional-differential equations with both continuous and discrete time variables. The goal of controlling the system under consideration is prescribed by a finite set of linear functionals. The number of these functionals is independent of the dimension of the system. We describe the subset of controls generated by a subsystem with the discrete time variable that solve the stated problems. DOI: 10.3103/S1066369X12090083

Inversion of linear delay dynamical systems

We consider the problem of inversion of a dynamical system, that is, the problem of real-time reconstruction of the unknown input of the system on the basis of measurements of its output. We consider linear systems of functional-differential equations in the case of commensurable delays. We obtain necessary conditions for the invertibility of this class of systems and suggest an inversion algorithm that permits one to obtain an estimate of the unknown input signal with given accuracy.

Some Exact Conditions for the Solvability of the Initial-Value Problem for Systems of Linear Functional-Differential Equations

We obtain exact, in a sense, conditions sufficient for the unique solvability of the Cauchy problem for systems of linear functional-differential equations of the general form. Efficient criteria for the unique solvability of the initial-value problem for systems of equations with deviating argument are given.

Some new conditions for the solvability of the Cauchy problem for systems of linear functional-differential equations

We establish efficient conditions sufficient for the unique solvability of certain classes of Cauchy problems for systems of linear functional-differential equations. The conditions obtained are optimal in a certain sense.

Some new conditions for the solvability of the cauchy problem for systems of linear functional-differential equations

Some new conditions for the solvability of the cauchy problem for systems of linear functional-differential equations

Some new conditions for the solvability of the cauchy problem for systems of linear functional-differential equations

Some new conditions for the solvability of the cauchy problem for systems of linear functional-differential equations

Exact Solvability Conditions for the Cauchy Problem for Systems of First-Order Linear Functional-Differential Equations Determined by ( 1, σ2, … , σn; )-Positive Operators

We obtain new sufficient conditions under which the Cauchy problem for a system of linear functional-differential equations is uniquely solvable for arbitrary forcing terms. The conditions established are unimprovable in a certain sense.

Continuability of Analytic Solutions of Some Linear Systems of Functional-Differential Equations

Continuability of Analytic Solutions of Some Linear Systems of Functional-Differential Equations

Quasi-periodic solutions of a linear functional-differential equation

We use the Kolmogorov-Arnol'd-Moser method to establish the existence of an n-parameter family of quasi-periodic solutions of a system of linear functional-differential equations.

Singular analytic solutions to some linear systems of functional-differential equations in a neighborhood of a regular singularity

Singular analytic solutions to some linear systems of functional-differential equations in a neighborhood of a regular singularity

Stability estimates of solutions of systems of functional-differential equations of neutral type

A system of linear functional-differential equations of neutral type is considered. Investigation of stability is carried out by the method of Lyapunov functions of quadratic form. Sufficient conditions for the asymptotic stability and estimates of the exponential decay of solutions for an arbitrary and a small deviation of the argument are obtained.