Yawvi A. Fiagbedzi

Feedback stabilization of neutral systems via the transformation technique

Within the class of delay systems, a neutral system may be distinguished by the possible presence of a neutral root chain—an infinite chain of eigenvalues in a vertical strip of the complex plane. Assuming that such a neutral root chain, if it exists, is stable, this work shows how our method of transformation can be extended to obtain feedback controllers for this class of neutral systems.

Finite-dimensional observers for delay systems

A finite-dimensional observer theory is formulated for a class of point delayed systems. The observer is characterized by the fact that it directly generates a finite-dimensional feedback controller for this class of systems. The theory is based on a preliminary approximation theory which allows the delay system to be exponentially approximated by a system of ordinary differential equations.

Characterization of small solutions in functional differential equations

Abstract A characterization is given of the initial functions which yield small solutions in a class of linear, autonomous, retarded functional differential equations.

Finite-dimensional representation of delay systems

Abstract It is shown that given a state delayed system, one can construct a finite-dimensional system whose partial state replicates the response of the delay system up to a small solution of the homogeneous delay system. Thus, in the absence of small solutions, the response of the delay system can be exactly replicated by a finite-dimensional system. reserved.

Finite‐dimensional approximation of neutral systems with v 0 ‐stable root chains

Here, t > 0 denotes time, 0< r < ∞ denotes the memory span while the state matricesA−1, A0, A1 ∈ Rn×n and the control matrixB0 ∈ Rn×m . The control function u ∈ L loc 1 ([0, ∞); Rm) andx(t) ∈ Rn . In what follows, the notation(SN , φ) is employed to represent the initial value problem (IVP) defined by (1.1), (1.2). The solution of the IVP (SN , φ) is given by Hale (1977, Theorem 7.1, p.25) as follows: There exists a unique continuously differentiable functionx : (−∞, ∞) → Rn which coincides withφ on [−r, 0] and satisfies (1.1) except possibly at {kr}k∈Z whereZ is the set of integers. For t 0, xt (θ; φ) x(t + θ), −r θ 0, represents the state of (SN , φ). Let ν0 0 be specified. DefineC + −ν0 = {s ∈ C : Res −ν0} as the closed right half of the complex plane bounded by Re s = −ν0 and its complement inC as

Finite Dimensional Representation of Distributed Delay Systems

It is shown that a class of distributed delay systems can be represented by a system of ordinary differential equations with arbitrary degree of accuracy.

Periodic solutions of retarded functional differential equations

Abstract. The classical criterion for the existence of a periodic solution of a forced, linear, retarded functional differential equation (rfde) references the solution of an adjoint equation which is an advanced functional differential equation. This paper introduces a new criterion which does away with the (anti-causal) advanced functional differential equation.

Stabilization of structurally damped systems by pointwise time-delayed feedback control

Abstract A class of multi-dimensional damped distributed parameter systems with pointwise time-delayed displacement is considered. The linear systems with delayed control action are transformed into equivalent systems without delays. It is shown that the feedback gain control exists and asymptotically stabilizes the closed-loop modal system. An analysis of the effectiveness of using pointwise time-delayed displacement under these condition is studied. Specific numerical results are given for a structurally damped beam for various parameters when the pointwise delayed displacement feedback control is applied.

A perturbation approach to finite dimensional stabilization of time-lag systems

A finite dimensional state variable feedback controller is proposed for time-lag systems described by differential-difference equations. The result is made explicit for scalar systems.