Optimal time-variant systems and factorization of operators, II: Factorization.
Дамир Зямович Аров, M. A. Kaashoek, Derk Pik · 2000
Abstract. For a block lower triangular contraction T the maximal block lower triangular outer solutions F and G of the operator inequalities I − T ∗T> F ∗F, and I − TT ∗> GG ∗ are identified in terms of optimal and star-optimal time-variant realizations of T, respectively. Special attention is given to the case when the inequality I − T ∗T> F ∗F is satisfied for F = 0 only, and to the case when equality can be obtained. As a byproduct a characterization is derived of optimality of a time-variant system in terms of the input coefficients of the systems only. The existence of maximal block lower triangular solutions F of the operator inequality I − T ∗T> F ∗F is also used to derive an optimal realization of T.