DocumentCode :
1411514
Title :
The gain scheduling and the robust state feedback stabilization problems
Author :
Blanchini, F.
Author_Institution :
Dipartimento di Matematica e Inf., Udine Univ., Italy
Volume :
45
Issue :
11
fYear :
2000
fDate :
11/1/2000 12:00:00 AM
Firstpage :
2061
Lastpage :
2070
Abstract :
We consider dynamical uncertain systems of the form x˙=a(x, w)+b(x, w)u where w(t)∈W is an unknown but bounded time-varying parameter. We consider the robust state feedback stabilization problem, in which we consider a control of the form u=Φ(x), and the gain-scheduling stabilization problem in which a control of the form u=Φ(x, w) (full information control) is admitted. We show that for convex processes, those systems in which for fixed x the set of all [a(x, w)b(x, w)] is convex, the two problems are equivalent; i.e., if there exists a (locally Lipschitz) gain scheduling stabilizing control then there exists a robustly stabilizing control (continuous everywhere except possibly at the origin). Thus, for convex process stabilization, knowledge of w(t) is not an advantage for the compensator. Then we consider the special class of polytopic LPV systems, and show that there is no loss of regularity as in the general case, if we pass from a gain-scheduling controller to a state feedback controller. In particular, no discontinuity at the origin may occur. We show that the existence of a dynamic controller always implies the existence of a static one. Finally we show that we can always find a linear gain-scheduling controller for a stabilizable system. This means that a possible advantage of the online measurement of the parameter w(t) is that this always allows for linear compensators, whose implementation can be easier than that of nonlinear ones.
Keywords :
compensation; robust control; state feedback; time-varying systems; uncertain systems; convex process stabilization; dynamical uncertain systems; linear compensators; linear gain-scheduling controller; locally Lipschitz gain scheduling stabilizing control; polytopic LPV systems; robust state feedback stabilization; unknown bounded time-varying parameter; Control design; Control systems; Nonlinear control systems; Nonlinear dynamical systems; Robust control; Robustness; Stability analysis; State feedback; Uncertain systems;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/9.887627
Filename :
887627
Link To Document :
بازگشت