The analysis of time-varying control for robust stabilization and performance improvement is considered. This problem has been investigated in recent years from the point of view of assessing the capabilities of time-varying control to stabilize plants with structured norm bounded perturbations. In this paper, it is shown that time-varying compensation provides no improvement over time-invariant compensation for the stability and performance robustness of discrete-time systems with structured, causal, time-varying, and norm-bounded perturbations, where the norm on the perturbations is the l2-induced norm. The results of this paper help in completing the picture for the case of time-varying perturbations.

Issue Section:
Technical Briefs
Topics:
Stability, Discrete time systems, Robustness
1.
Chapellat
H.
, and
Dahleh
M.
,
1992
, “
Analysis of Time-Varying Control Strategies for Optimal Disturbance Rejection and Robustness
,”
IEEE Trans. on Automatic Control
, Vol.
37
, No.
11
, Nov., pp.
1734
–
1745
.
2.
Khammash
M.
, and
Dahleh
M.
,
1992
, “
Time-Varying Control and the Robust Performance of Systems with Structured Norm-Bounded Perturbations
,”
Automatica
, Vol.
28
, No, 4, July, pp.
819
–
821
.
3.
Khargonekar, P. P., and Poolla, K., 1989, “Robust Control of Linear Time-Invariant Plants Using Switching and Nonlinear Feedback,” Proceedings of the 28th Conference on Decision and Control, Tampa, FL, pp. 2205–2207.
4.
Shamma
J. S.
, and
Dahleh
M. A.
,
1991
, “
Time-Varying vs. Time-Invariant Compensation for Rejection of Persistent Bounded Disturbances and Robust Stabilization
,”
IEEE Trans. Automat. Contr.
, Vol.
AC-36
, pp.
838
–
847
.
5.
Shamma, J. S., 1992, “Robust Stability with Time-Varying Structured Uncertainty,” to appear in 31st IEEE Conference on Decision and Control.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.