Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Functions of One Complex Variable

Functions of one complex variable II

Stability and stabilization of infinite dimensional systems with applications

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Introduction To Infinite Dimensional Linear Systems Theory

https://hal.archives-ouvertes.fr/hal-00819133/document

Stability analysis of neutral type systems in Hilbert space

We study problems of boundary controllability with minimal Lp--norm ($p\in [2,\infty]$) for the one-dimensional wave equation, where the state is controlled at both boundaries through Dirichlet or Neumann conditions. The problem is to reach a given terminal state and velocity in a given finite time, while minimizing the Lp--norm of the controls. We give necessary and sufficient conditions for the solvability of this problem. We show as follows how this infinite-dimensional optimization problem can be transformed into a problem which is much simpler: The feasible set of the transformed problem is described by a finite number of simple pointwise equality constraints for the control function in the Dirichlet case while, in the Neumann case, an additional integral equality constraint appears. We provide explicit complete solutions of the problems for all $p\in[2,\infty]$ in the Dirichlet case and solutions for some typical examples in the Neumann case.

L p -Optimal Boundary Control for the Wave Equation

The problem of exact null-controllability is considered for a wide class of linear neutral-type systems with distributed delay. The main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families. A complete characterization of this problem is given. The minimal time of controllability is specified. The results are based on the analysis of the Riesz basis property of eigenspaces of the neutral-type systems in Hilbert space.

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The Analysis of Exact Controllability of Neutral-Type Systems by the Moment Problem Approach

https://hal.archives-ouvertes.fr/hal-00819154/document

Generalized Riesz basis property in the analysis of neutral type systems

We consider a slowly rotating Timoshenko beam in a horizontal plane whose movement is controlled by the angular acceleration of the disk of a driving motor into which the beam is clamped. The problem to be solved is to transfer the beam from a position of rest into a position of rest under a given angle within a given time. We show that this problem is solvable, if the time of rotation prescribed is large enough.

https://www.ems-ph.org/journals/show_pdf.php?issn=0232-2064&vol=18&iss=2&rank=17

Grigory M. Sklyar

Papers

Stability analysis of neutral type systems in Hilbert space

L p -Optimal Boundary Control for the Wave Equation

The Analysis of Exact Controllability of Neutral-Type Systems by the Moment Problem Approach

Generalized Riesz basis property in the analysis of neutral type systems

On the Controllability of a Slowly Rotating Timoshenko Beam