In this paper, the state-feedback mixed H2/H control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

1.
He
,
J.-B.
,
Wang
,
Q.-G.
, and
Lee
,
T.-H.
,
1998
, “
H∞ Disturbance Attenuation for State Delayed Systems
,”
Syst. Control Lett.
,
33
, pp.
105
114
.
2.
Hwa Lee
,
J.
,
Woo Kim
,
S.
, and
Hyun Kwon
,
W.
,
1994
, “
Memoryless H∞ Controllers for State Delayed Systems
,”
IEEE Trans. Autom. Control
,
39
(
1
), pp.
159
162
.
3.
Mahmood
,
M. S.
, and
Muthairi
,
N. F.
,
1994
, “
Quadratic Stabilization of Continuous-Time Systems With State-Delay and Norm-Bounded Time-Varying Uncertainties
,”
IEEE Trans. Autom. Control
,
39
(
11
), pp.
2135
2140
.
4.
Phoojaruenchanachai
,
S.
, and
Furuta
,
K.
,
1992
, “
Memoryless Stabilization of Uncertain Linear Systems Including Time-Varying State Delays
,”
IEEE Trans. Autom. Control
,
37
(
7
), pp.
1020
1026
.
5.
Meinsma
,
G.
, and
Zwart
,
H.
,
2000
, “
On H∞ Control for Dead-Time Systems
,”
IEEE Trans. Autom. Control
,
45
(
2
), pp.
272
285
.
6.
Bernstein
,
D. S.
, and
Haddad
,
W. M.
,
1989
, “
LQG Control with H∞ Performance Bound
,”
IEEE Trans. Autom. Control
,
34
(
3
), pp.
293
305
.
7.
Khargonekar
,
P. P.
, and
Rotea
,
M. A.
,
1991
, “
Mixed H2/H∞ Control: A Convex Approach
,”
IEEE Trans. Autom. Control
,
36
(
7
), pp.
824
837
.
8.
Limebeer
,
D. J. N.
,
Anderson
,
B. D. O.
, and
Hendel
,
B.
,
1994
, “
A Nash Game Approach to Mixed H2/H∞ Control
,”
IEEE Trans. Autom. Control
,
39
(
1
), pp.
262
283
.
9.
Basar, T., and Bernhard, P., 1991, H∞. Optimal Control and Related Minimax Design, Birkhauser, New York.
10.
Gahinet, P., Nemirovsky, A., Laub, A. J., and Hilali, M., 1995, LMI Control Toolbox, Mathworks Inc. Mass.
11.
Lee, E. B., and Markus, L., 1967, Foundation of Optimal Control, SIAM Series on Applied Mathematics, John Wiley & Sons Inc., New York.
12.
Boyd, S., Ghaoui, L. E., Feron, E., and Balakhrishnan, V., 1994, Linear Matrix Inequalities in Systems and Control Theory, SIAM Series in Systems and Control, Philadelphia.
13.
Frieling
,
G.
,
Jank
,
G.
, and
Abou-kandil
,
H.
,
1996
, “
On the Global Existence of Solutions to Coupled Matrix Riccati Equations in Closed-Loop Nash Games
,”
IEEE Trans. Autom. Control
,
41
(
2
), pp.
264
269
.
14.
Zhou, K., Doyle, J. C., and Glover, K., 1996, Robust and Optimal Control, Prentice Hall, New Jersey.
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