Finite spectrum assignment problem for a delay type system

For a spectrally controlled linear time-invariant delay system with commensurable delays, we construct a static state feedback ensuring an arbitrary finite spectrum of the closedloop system. By an appropriate choice of the spectrum, one can make the closed-loop system asymptotically stable. The results are illustrated by examples.     

Spectral reduction, complete damping, and stabilization of a delay system by a single controller

For a spectrally controllable linear autonomous differential-difference system of retarded type, we construct a dynamic state feedback that provides the complete damping of the original system and a finite spectrum of the closed-loop system. The closed-loop system can be made asymptotically stable by an appropriate choice of the spectrum. The results are illustrated by examples.     

Complete damping of a linear autonomous differential-difference system by a controller of the same type

For a spectrally controllable linear autonomous system of retarded type with commensurable delays, we construct a dynamic state feedback ensuring a complete damping of the original system. The closed-loop system is of retarded type as well. The results are illustrated by an example.     

Bounds for the spectrum of a matrix differential operator with a damping term

We consider a second-order matrix ordinary regular differential nonselfadjoint operator with a damping term and selfadjoint boundary conditions. An estimate for the resolvent and bounds for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.     

Bounds for the spectrum of a matrix differential operator with a damping term

We consider a second-order matrix ordinary regular differential nonselfadjoint operator with a damping term and selfadjoint boundary conditions. An estimate for the resolvent and bounds for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.     

Eigenvalues and eigenvectors assignment for neutral type systems

For a class of linear neutral type systems, the problem of eigenvalues and eigenvectors assignment is investigated, i.e. the system that has the given spectrum and almost all, in some sense, eigenvectors is investigated. The result is used for the analysis of the critical number of solvability of a vector moment problem.     

Solution damping controllers for linear systems of the neutral type

For linear autonomous systems of the neutral type with commensurable delays in the state and control, we solve the problem of solution damping by a state feedback controller. In this case, the closed-loop system becomes a system of the neutral type with a finite spectrum. The present research is characterized by the fact that the original system does not necessarily have the property of complete controllability.     

Oscillation of differential systems of neutral type

We study oscillatory properties of solutions of systems

Asymptotic stability of differential systems of neutral type

We offer sufficient conditions for the asymptotic stability of the equilibrium point of linear neutral differential systems. An application of our results to a family of artificial neural networks of neutral type is also illustrated.     

On conditions for the discreteness of the spectrum of a non-self-adjoint system of differential equations of the Dirac type

A first-order non-self-adjoint system of differential equations with 2n unknown functions and with certain conditions on the coefficients is considered on the entire axis. The system is similar to the well-known Dirac system. An operator , associated with the considered system, is introduced in the space L²(– , ) of 2n-component vector-valued functions. Conditions for the compactness of the resolvent of the operator are found, yielding sufficient conditions for the discreteness of its spectrum.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 16, pp. 3–24, 1992.     

Lag synchronizing chaotic system based on a single controller

Lag synchronization of chaotic system is investigated. Three kinds of schemes are proposed to lag synchronize Chen chaotic system. All the three schemes need only a single controller to realize lag synchronization. Especially in the last two schemes, only one state variable is contained in controller, which is of important significance on using chaos lag synchronization for applications. Finally numerical simulations are provided to show the effectiveness of the developed methods.     

Oscillations of higher order differential equations of neutral type

In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of nth order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.     

Oscillatory behaviour in functional differential systems of neutral type

In this paper are obtained several criteria for oscillations of a class of autonomous functional differential systems of neutral type.