Optimization and Systems Theory Seminar
Monday, December 7, 1998, 11.00-12.00, Room 3733, Lindstedtsvägen 25
Dr. Bertina Ho-Mock-Qai
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 time-varying state feedback law which
exponentially asymptotically stabilizes all the systems in the family.
- We have obtained sufficient conditions for the existence of a
time-varying 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
time-invariant 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 time-varying
state feedback law which robustly exponentially stabilizes the family.
-
We have constructed continuous time-invariant feedback laws which
robustly stabilize certain uncountable families of 2-dimensional
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.