Impulse Controllability Problem for the Equation of a String with an External Load on a Rectangle QT = [0 ≤ x ≤ π] × [0 ≤ t ≤ T].

In this paper necessary and sufficient conditions for impulse null-controllability and approximate null-controllability are obtained for the controllability problem for the equation of the string on a rectangle. This article discusses control that is carried out using an external load. Controls solving these problems are found explicitly.

On Controllability for Linear Differential-Algebraic Control Systems Using Equivalent Form

We investigate different concepts related to the controllability of linear constant coefficient differentialalgebraic equations. Concepts like impulse controllability, controllability at infinity, strong and complete controllability are described and defined by using an equivalent form for linear time-invariant singular systems. Some real-life problems are given to illustrate the presented theory.

Impulsive Controllability/Observability for Interconnected Descriptor Systems with Two Subsystems

The problem of decentralized impulse controllability/observability for large-scale interconnected descriptor systems with two subsystems by derivative feedback is studied. Necessary conditions for the existence of a derivative feedback controller for the first subsystem of the large-scale interconnected descriptor systems ensuring the second subsystem to be impulse controllable and impulse observable are derived, respectively. Based on the results, a derivative feedback controller for the first subsystem of the large-scale interconnected descriptor systems is constructed easily such that the second subsystem is impulse controllable or impulse observable. Finally, examples are given to illustrate the effectiveness of the results obtained in this paper.