In this paper, we discuss the design of controllers that provide quadratic stability and a desirable disturbance attenuation level (through an appropriately small L2 gain) for systems with time varying, real and structured uncertainty. It is shown that for a class of systems, the problem of designing dynamic output feedback can be separated into two stages, each an easily solvable convex problem. This information could be used in system design and configuration. Two examples are presented to illustrate the proposed approach.

1.
Gahinet
P.
, and
Apkarian
P.
,
1994
, “
A Linear Matrix Inequality Approach to H Control
,”
Int. Jour. of Robust and Nonlinear Control
, Vol.
4
, pp.
421
448
.
2.
Galimidi
and
Barmish
,
1986
The Constrained Lyapunov Problem and its Application to Robust Output Feedback Stabilization
,”
IEEE Trans. on Automatic Control
, Vol.
31
, pp.
410
418
.
3.
Gu
K.
,
1994
, “
H Control of Systems Under Norm-Bounded Uncertainties in all System Matrices
,”
IEEE Trans. on Automatic Control
, Vol.
39
, No.
6
, pp.
1320
1322
.
4.
Iwasaki
T.
, and
Skelton
R.
,
1994
, “
All Controllers for the General H Control Problem: LMI Existence Conditions and State Space Formulas
,”
Automatica
, Vol.
30
, No.
8
, pp.
1307
1317
.
5.
Packard, A., Zhou K., Pandey, P., and Becker, G., 1991, “A Collection of Robust Control Problems Leading to LMIs,” Proc. of CDC, pp. 1245–1250.
6.
Rotea
M. A.
,
Corless
M.
,
Da
D.
, and
Petersen
I. R.
,
1993
, “
Systems with Structured Uncertainty: Relations Between Quadratic and Robust Stability
,”
IEEE Trans. on Automatic Control
, Vol.
38
, No.
5
, pp.
799
803
.
7.
Scorletti, G., El Ghaoui, L., 1995, “Improved Linear Matrix Inequality Conditions for Gain Scheduling,” Proc. of CDC, pp. 3626–3631.
8.
Xie
L.
,
Fu
M.
, and
de Souza
C. E.
,
1992
, “
H Control and Quadratic Stabilization of Systems with Parameter Uncertainty Via Output Feedback
,”
IEEE Trans. on Automatic Control
, Vol.
37
, pp.
1253
1256
.
9.
Zhou
K.
,
Khargonekar
P. P.
,
Stoustrup
J.
, and
Niemann
H. H.
,
1995
, “
Robust Performance of Systems with Structured Uncertainties in State Space
,”
Automatica
, Vol.
31
, pp.
249
255
.
This content is only available via PDF.
You do not currently have access to this content.