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Controlling a non-homogeneous Timoshenko beam with the aid of the torque

Sklyar G. M., Szkibiel G.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 3

587--598

Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C0-continuous semigroups may be applied.

Holdability and stabilizability of 2D Roesser model

Kaczorek T.

Control and Cybernetics

2003

Vol. 32, no 1

75-86

The holdability and stabilizability problem of 2D Roesser model is formulated and solved. Conditions for the existence of solution to the problem are established. Two procedures for computation of a gain matrix of the state-feedback are proposed and illustrated by a numerical example.

Sformułowano i rozwiązano zadanie utrzymywania i stabilizowalności dla dwuwymiarowego modelu Roessera. Ustalono warunki istnienia rozwiązania tego zadania. Zaproponowano dwie procedury wyliczania macierzy przejścia w pętli sprzężenia zwrotnego względem stanu i zilustrowano je przykładem numerycznym.