Full Text:   <1893>

CLC number: O224

On-line Access: 

Received: 2002-12-21

Revision Accepted: 2003-03-26

Crosschecked: 0000-00-00

Cited: 0

Clicked: 4017

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.1 P.68-74


A SISO mixed H2/l1 optimal control problem and its solution

Author(s):  WU Jun, HU Xie-he, CHU Jian

Affiliation(s):  National Key Laboratory of Industrial Control Technology, Institute of Advanced Process Control, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   jwu@iipc.zju.edu.cn

Key Words:  Mixed H2/l1 problem, Existence, Uniqueness, Approximation

Share this article to: More

WU Jun, HU Xie-he, CHU Jian. A SISO mixed H2/l1 optimal control problem and its solution[J]. Journal of Zhejiang University Science A, 2004, 5(1): 68-74.

@article{title="A SISO mixed H2/l1 optimal control problem and its solution",
author="WU Jun, HU Xie-he, CHU Jian",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T A SISO mixed H2/l1 optimal control problem and its solution
%A WU Jun
%A HU Xie-he
%A CHU Jian
%J Journal of Zhejiang University SCIENCE A
%V 5
%N 1
%P 68-74
%@ 1869-1951
%D 2004
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2004.0068

T1 - A SISO mixed H2/l1 optimal control problem and its solution
A1 - WU Jun
A1 - HU Xie-he
A1 - CHU Jian
J0 - Journal of Zhejiang University Science A
VL - 5
IS - 1
SP - 68
EP - 74
%@ 1869-1951
Y1 - 2004
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2004.0068

Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptimal solutions and solvable superoptimal solutions.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Boyd, S.P., Balakrishnan, V. and Barratt, C.H., 1988. A new CAD method and associate architecture for linear controllers. IEEE Trans. Automat. Contr., 33(3):268-283.

[2] Cohen, A. and Shaked, U., 1997. Robust discrete-time H2 control. International Journal of Control, 67(2):213-232.

[3] Conway, J.B., 1990. A Course in Functional Analysis. Springer-Verlag, New York.

[4] Dahleh, M.A., 1992. BIBO stability robustness for coprime factor perturbations. IEEE Trans. Automat. Contr., 37(3):352-355.

[5] Dahleh, M.A. and Khammash, M., 1993. Controller design for plants with structured uncertainty. Automatica, 29(1):37-56.

[6] Dahleh, M.A. and Diaz-Bobillo, I.J., 1995. Control of Uncertain Systems: A Linear Programming Approach. Prentice Hall, New Jersey.

[7] Doyle, J.C., 1982. Analysis of feedback systems with structured uncertainty. Proceedings of the Institution of Electrical Engineers, Pt D, 129(6):242-250.

[8] Elia, N. and Dahleh, M.A., 1997. Controller design with multiple objectives. IEEE Trans. Automat. Contr., 42(5):596-613.

[9] Francis, B.A., 1987. A Course in H Control Theory. Springer-Verlag, Berlin.

[10] Jacques, D.R. and Ridgely, D.B., 1995. A Fixed-Order, Mixed-Norm Control Synthesis Method for Discrete Linear Systems. Proc. Amer. Contr. Conf., Seattle, p.1936-1940.

[11] Jacques, D.R., Canfield, R.A.and Ridgely, D.B., 1996. A MATLAB toolbox for fixed-order, mixed-norm control synthesis. IEEE Control Systems Magazine, 16(5):36-43.

[12] Kaminer, I., Khargonekar, P.P. and Rotea, M.A., 1993. Mixed H2/H control for discrete time systems via convex optimization. Automatica, 29(1):57-70.

[13] McDonald, J.S. and Pearson, J.B., 1991. l1 optimal control of multivariable systems with output norm constraints. Automatica, 27(2):317-329.

[14] Salapaka, M.V., Dahleh, M. and Voulgaris, P., 1995a. Mixed Objective Control Synthesis: Optimal l1/H2 Control. Proc. Amer. Contr. Conf., Seattle, p.1438-1442.

[15] Salapaka, M.V., Dahleh, M. and Voulgaris, P., 1995b. MIMO Optimal Control Design: The Interplay of the H2 and the l1 norms. Proc. IEEE Conf. Decision and Control, New Orleans, p.3682-3687.

[16] Staffans, O.J., 1993. The four-block model matching problem in l1 and infinite-dimensional linear programming. SIAM J. Contr. Optim., 31(3):747-779.

[17] Voulgaris, P., 1994. Optimal H2/l1 Control: the SISO Case. Proc. IEEE Conf. Decision and Control, Orlando, 4:3181-3186.

[18] Voulgaris, P., 1995. Optimal H2/l1 control via duality theory. IEEE Trans. Automat. Contr, 40(11):1881-1888.

[19] Wu, J. and Chu, J., 1996. Mixed H2/l1 Control for Discrete Time Systems. Proc. 13th IFAC Congress, San Francisco, G:453-457.

[20] Wu, J. and Chu, J., 1999. Approximation methods of scalar mixed H2/l1 problem for discrete time systems. IEEE Trans. Automat. Contr., 44(10):1869-1874.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE