In this paper we obtain a new formula for the minimum achievable disturbance attenuation in two-block H∞ problems.
This new formula has the same structure as the optimal H∞ 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 us to find explicit expressions for the optimal H∞ norm in several important cases: the equalization problem (or its dual, the tracking problem), and the problem of filtering signals in additive noise. Furthermore, it leads us to the concepts of “worst-case non-estimability”, corresponding to when causal filters cannot reduce the H∞ norms from their a priori values, and “worst-case complete estimability”, corresponding to when causal filters offer the same H∞ 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]
Edmond A. Jonckheere,et al.
L∞-compensation with mixed sensitivity as a broadband matching problem
,
1984
.
[2]
Z. Nehari.
On Bounded Bilinear Forms
,
1957
.
[3]
P. Khargonekar,et al.
State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
,
1989
.
[4]
P. Khargonekar,et al.
State-space solutions to standard H2 and H∞ control problems
,
1988,
1988 American Control Conference.
[5]
Edmond A. Jonckheere,et al.
A spectral characterization of H ∞ -optimal feedback performance and its efficient computation
,
1986
.