### Optimization and Systems Theory Seminar

Thursday, October 11, 2001, 13.15-14.15, Room 3721, Lindstedtsvägen
25

** Professor Vladimir A. Yakubovich**

St. Petersburg State University

St. Petersburg

Russia

####
Design of stabilizing controllers with system output independent of
external disturbance

The problem of the design of a universal controller that makes the
output of a control system invariant under any external disturbance
has a long history. Before the Second World War a discussion about
the possibility of developing such controllers took place among
Russian specialists in control theory. The special commission of the
Russian Academy of Sciences considered the arguments of the disputing
sides. After the Second World War regular conferences on this subject
were held in Russia.
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).

Calendar of seminars

*Last update: October 2, 2001 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*