This paper presents the results of robust filtering for a class of interconnected uncertain systems under sampled measurements. We address the problem of designing filters, using sampled measurements, which would guarantee a prescribed H∞ performance in the continuous-time context, irrespective of the parameter uncertainty and unknown initial states. Both the cases of finite and infinite horizon filtering are investigated in terms of N pairs of Riccati equations with finite discrete jumps.

Issue Section:
Technical Briefs
Topics:
Filtration, Uncertain systems, Design, Filters, Uncertainty
1.
Boyd, S., L. E, Ghaoui, E. Feron and V. Balakrishnan, (1994), “Linear Matrix Inequalities in System and Control Theory,” SIAM, Philadelphia.
2.
Fu
M.
, (
1991
), “
Interpolation Approach to H∞ Optimal Estimation and Its Interconnection to Loop Transfer Recovery
,”
System & Control Letters
, Vol.
17
(
1
), pp.
29
–
36
.
3.
Grimble, M. J., (1988), “H∞ Design of Optimal Linear Filters, in Linear Circ, Syst. and Signal Processing: Theory and Application, C. I. Byrnes, C. F. Martin and R. E. Sacks, eds., pp. 533–540, North-Holland, Amsterdam.
4.
Khargonekar
P. P.
,
Petersen
I. R.
and
Zhou
K.
, (
1991
), “
Robust Stabilization of Uncertain Linear Systems: Quadratic Stabilizability and H∞ Control Theory
,”
IEEE Trans. Automat. Control
, Vol.
35
(
3
), pp.
356
–
361
.
5.
Nagpal
K. M.
, and
Khargonekar
P. P.
, (
1991
), “
Filtering and Smoothing in an H∞ Setting
.”
IEEE Trans. Automat. Control
, Vol.
36
(
2
), pp.
152
–
166
.
6.
Shi, P., C. E. de Souza and L. Xie, (1993), “Robust H∞ Filtering for Uncertain Systems with Sampled-Data Measurements,” Proc. 32nd IEEE Conf. Decision & Control, pp. 793–798, San Antonio, Texas.
7.
Shi, P., C. E. de Souza and L. Xie, (1996), “Bounded Real Lemma for Linear Systems with Finite Discrete Jumps,” Int. J. Control, to appear.
8.
Sun
W.
,
Nagpal
K. M.
and
Khargonekar
P. P.
, (
1993
), “
H∞ Control and Filtering for Sampled-Data Systems
,”
IEEE Trans. Automat. Control
, Vol.
38
(
8
), pp.
1162
–
1175
.
9.
Xie, L., (1991), “H∞ Control and Filtering of Systems with Parameter Uncertainty, PhD thesis, The University of Newcastle, Australia.
10.
Xie
L.
,
de Souza
C. E.
, and
Fragoso
M. D.
, (
1991
), “
H∞ Filtering for Linear Periodic Systems with Parameter Uncertainty
,”
System & Control Letters
, Vol.
17
(
5
), pp.
343
–
350
.
11.
Yaesh
I.
, and
Shaked
U.
, (
1991
), “
A Transfer Function Approach to the Problems of Discrete-Time H∞ Optimal Control and Filtering
,”
IEEE Trans. Automat. Control
, Vol.
36
(
11
), pp.
1264
–
1271
.
This content is only available via PDF.
Copyright © 1997
 by The American Society of Mechanical Engineers
You do not currently have access to this content.