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On an Invariant Design of Feedbacks for Bilinear Control Systems of Second Order

Belozyorov V. Y.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 2

377-389

The problem of linear feedback design for bilinear control systems guaranteeing their conditional closed-loop stability is considered. It is shown that this problem can be reduced to investigating the conditional stability of solutions of quadratic systems of differential equations depending on parameters of the control law. Sufficient conditions for stability in the cone of a homogeneous quadratic system are obtained. For second-order systems, invariant conditions of conditional asymptotic stability are found.

A Stabilizing Control Law for Invariant Systems on Lie Groups

Apostolou N., Kazakos D.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 2

273-282

This paper deals with the stabilizability of invariant control systems defined on Lie groups. A stabilization technique is presented which, under certain hypotheses, can lead to a criterion assuring the existence of a feedback controller which steers every initial condition to a specified target point of the state space of these systems.