This paper focuses on the analysis and synthesis of a robust stabilizing controller for linear discrete time systems with norm-bounded time varying uncertainties. Delay independent robust stability conditions are derived and two synthesis methods are presented. One method is to construct a robust memoryless state feedback control law from the solutions of linear matrix inequalities. The other method consists of designing robust observer-based output feedback controller. The results are expressed in termes of linear matrix inequalities. A comparison with μ∕LDI tests is presented. Furthermore, numerical examples are given for illustration.

Issue Section:
Technical Briefs
Keywords:
discrete time systems, robust stability, robust stabilization, observer-based output feedback, linear matrix inequalities, robust control, control system synthesis, discrete time systems, time-varying systems, state feedback, linear matrix inequalities, observers
Topics:
Delays, Design, Discrete time systems, Feedback, Linear matrix inequalities, Robust control, Stability, State feedback, Uncertainty, Control equipment
1.
Su
,
T. J.
, and
Shyr
,
W. J.
, 1994, “
Robust D-Stability for Linear Uncertain Discrete Delay Systems
,”
IEEE Trans. Autom. Control
0018-9286,
39
, pp.
425
–
428
.
2.
Hmamed
,
A.
, and
Tissir
,
E.
, 1998, “
Further Results on the Stability of Discrete Time Matrix Polynomials,”
Int. J. Syst. Sci.
0020-7721,
29
, pp.
819
–
821
.
Crossref
Search ADS
 
3.
Hmamed
,
A.
, and
Tissir
,
E.
, 1998, “
D-stabilité des matrices polynomiales dans les systèmes discrets,”
in
Proc. Conf. Méditérranèene sur l"Electronique et l"Automatique
, Marrakech, pp.
89
–
92
.
4.
Wu
,
J. W.
, and
Hong
,
K. S.
, 1994, “
Delay Independent Exponential Stability Criteria for Time Varying Discrete Delay Systems,”
IEEE Trans. Autom. Control
0018-9286,
49
, pp.
811
–
814
.
5.
Mori
,
T.
,
Fukuma
,
N.
, and
Kuwahara
,
M.
, 1982, “
Delay Independent Stability Criteria for Discrete Delay Systems,”
IEEE Trans. Autom. Control
0018-9286,
27
, pp.
964
–
966
.
Crossref
Search ADS
 
6.
Lee
,
C. H.
,
Li
,
T. H. S.
, and
Kung
,
F. C.
, 1992, “
D-Stability Analysis for Discrete Systems With Time Delay
,”
Syst. Control Lett.
0167-6911,
19
, pp.
213
–
219
.
Crossref
Search ADS
 
7.
Lee
T. N.
, and
Radovic
,
U. L.
, 1987, “
General Decentralized Stabilization of Large Scale Linear Continuous and Discrete Time Systems
,”
Int. J. Control
0020-7179,
46
, pp.
2127
–
2140
.
Crossref
Search ADS
 
8.
Boyd
,
S.
,
ELGhaoui
,
L.
,
Feron
,
E.
, and
Balakrishnan
,
V.
, 1994, “
Linear Matrix Inequalities in Systems and Control Theory
,”
Stud. Appl. Math.
0022-2526,
15
.
9.
Nesterov
,
Y.
, and
Nemirovsky
,
A.
, 1994, “
Interior Point Polynomial Methods in Convex Programming
,”
Stud. Appl. Math.
0022-2526,
13
.
10.
Vandenberghe
,
L.
, and
Boyd
,
S.
, 1995, “
Primal-Dual Potential Reduction Method for Problems Involving Matrix Inequalities
,”
Math. Program.
0025-5610,
69
, pp.
205
–
236
.
11.
Wang
,
Y.
,
Xie
,
L.
, and
de Souza
,
C. E.
, 1992, “
Robust Control of a Class of Uncertain Nonlinear Systems
,”
Syst. Control Lett.
0167-6911,
19
, pp.
139
–
149
.
Crossref
Search ADS
 
12.
Horn
,
R. A.
, and
Johnson
,
C. R.
, 1985,
Matrix Analysis
,
Cambridge Uni. Pr.
,
Cambridge, UK
.
13.
Packard
,
A.
, and
Doyle
,
J. C.
, 1993, “
The Complex Structured Singular Value
,”
Automatica
0005-1098,
29
(
1
), pp.
71
–
109
.
Crossref
Search ADS
 
Copyright © 2007
 by American Society of Mechanical Engineers
You do not currently have access to this content.