A solution is obtained to the infinite time optimal tracking problem for a multivariable system. The derivation is more direct than the usual approach through Parseval's theorem and it relates Hilbert space gradient techniques to the complex frequency domain.
where W * : Ln2 (0, ∞) → L m2 (- ∞, ∞). By considering the properties of the impulse response matrix it may be confirmed that the system represented by the operator W * has a response (W*y) (t) existing for negative time, even though y is zero for negative time. It is clear that W * represents a non-causal system.
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