Issue |
ESAIM: COCV
Volume 6, 2001
|
|
---|---|---|
Page(s) | 291 - 331 | |
DOI | https://doi.org/10.1051/cocv:2001112 | |
Published online | 15 August 2002 |
On the Lp-stabilization of the double integrator subject to input saturation
Université Paris XI,
Département de Mathématiques, 91405 Orsay, France;
Yacine.Chitour@math.u-psud.fr.
Received:
22
November
1999
Received:
January
2001
We consider a finite-dimensional control system , such that there exists a feedback stabilizer k
that renders
globally asymptotically
stable. Moreover, for (H,p,q) with H an output map and
, we assume that there exists a
-function
α such that
, where xu is the
maximal solution of
,
corresponding to u and to the initial condition x(0)=0. Then, the
gain function
of (H,p,q) given by 14.5cm
is well-defined. We call profile of k for (H,p,q) any
-function which is of the same order of magnitude
as
. For the double integrator subject to input saturation
and stabilized by
, we determine the profiles corresponding to the main
output maps. In particular, if
is used to denote the standard
saturation function, we show that the L2-gain from the output of the
saturation nonlinearity to u of the system
with
, is finite. We also provide a class of feedback
stabilizers kF that have a linear profile for (x,p,p),
.
For instance,
we show that the L2-gains from x and
to u of the
system
with
,
are finite.
Mathematics Subject Classification: 93D15 / 93D21 / 93D30
Key words: Nonlinear control systems / Lp-stabilization / input-to-state stability / finite-gain stability / input saturation / Lyapunov function.
© EDP Sciences, SMAI, 2001
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