Optimization and Systems Theory Seminar
Monday, December 7, 1998, 11.0012.00, Room 3733, Lindstedtsvägen 25
Dr. Bertina HoMockQai
Centre d'Etudes de la Navigation Aerienne
Toulouse, France
A nonlinear approach to robust stabilization
The robust stabilization of a family of control systems consists in finding a
control law which stabilizes all the systems in the family.
We present a new approach to robust stabilization which enables us to
establish the following results:
Countable families of systems

Given any countable family of general nonlinear systems,
that can be individually asymptotically stabilized, there exists a $C^0$
state feedback law which stabilizes (not asymptotically) all the systems
in the family.

Given any finite family of stabilizable LTI
(linear time invariant) systems, there
exists a $C^0$ nonlinear timevarying state feedback law which
exponentially asymptotically stabilizes all the systems in the family.
 We have obtained sufficient conditions for the existence of a
timevarying feedback law which asymptotically stabilizes all the systems
of a finite family of nonlinear systems.
Uncountable families of systems

Given any family of stabilizable LTI systems
which depends continuously on real parameters
that lie in closed intervals, there exists a continuous nonlinear
timeinvariant state feedback law which stabilizes (not asymptotically)
all the systems in the family.

Given any family of stabilizable LTI systems
which depends continuously on real parameters
that lie in closed intervals, there exists a continuous nonlinear timevarying
state feedback law which robustly exponentially stabilizes the family.

We have constructed continuous timeinvariant feedback laws which
robustly stabilize certain uncountable families of 2dimensional
nonlinear systems, which cannot be robustly stabilized by means of
$C^1$ feedback.
Calendar of seminars
Last update: December 3, 1998 by
Anders Forsgren,
andersf@math.kth.se.