Professor Vladimir A. Yakubovich
St. Petersburg State University
In this talk a variant of this problem is considered. The simple formulas are obtained describing the set of all stabilizing controllers for the minimum-phase object. It is shown that the absolute invariance is possible under some conditions if the external disturbance is measured and if it is one of the inputs of the controller. It is also proved that the absolute invariance is impossible if the external disturbance is not measured. ( An example of the first case is the problem of automatic car steering.) It is shown that in the second case the approximate solution of the invariance problem is possible (with any precision) if the external disturbances belong to some sufficiently general classes. As an example of the second case the approach problem is considered (one moving object must approach the other).