We obtain a new formula for the minimum achievable disturbance attenuation in two-block H/sup /spl infin// problems. This new formula has the same structure as the optimal H/sup /spl infin// norm formula for noncausal problems, except that doubly-infinite (so-called Laurent) operators must be replaced by semi-infinite (so-called Toeplitz) operators. The benefit of the new formula is that it allows one to find explicit expressions for the optimal H/sup /spl infin// norm in several important cases: the equalization problem, and the problem of filtering signals in additive noise. Furthermore, it leads one to the concepts of "worst-case non-estimability", corresponding to when causal filters cannot reduce the H/sup /spl infin// norms from their a priori values, and "worst-case complete estimability", corresponding to when causal filters offer the same H/sup /spl infin// performance as noncausal ones. We also obtain an explicit characterization of worst-case non-estimability and study the consequences to the problem of equalization with finite delay.
[1]
P. Khargonekar,et al.
State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
,
1989
.
[2]
P. Khargonekar,et al.
State-space solutions to standard H2 and H∞ control problems
,
1988,
1988 American Control Conference.
[3]
Bruce A. Francis,et al.
Uniformly optimal control of linear feedback systems
,
1985,
Autom..
[4]
A. Erdogan,et al.
Equalization with an H 1 Criterion
,
1997
.
[5]
Edmond A. Jonckheere,et al.
A spectral characterization of H ∞ -optimal feedback performance and its efficient computation
,
1986
.
[6]
Thomas Kailath,et al.
Equalization with an H" Criterion'
,
1998
.
[7]
Z. Nehari.
On Bounded Bilinear Forms
,
1957
.
[8]
Edmond A. Jonckheere,et al.
L∞-compensation with mixed sensitivity as a broadband matching problem
,
1984
.