Dieter rer. nat. Prätzel-Wolters

Parametrization of (C,A)-invariant subspaces

In this paper we classify and parametrize the ( C,A )-invariant subspaces of a given observable pair ( C,A ). For that purpose we associate with every ( C,A )-invariant subspace V a K [ s ]-module M V of Laurent series in s −1 and parametrize these modules via their uniquely determined Kronecker-Hermite bases. The discrete and continuous parameters thus obtained are interpreted in slate space terms. Finally we illustrate the results by presenting a complete overview over the set of all ( C,A -invariant subspaces for a given pair ( C,A )∈ℝ 6 × (3 + 6) in dual Brunovsky canonical form.

The Bruhat decomposition of finite Hankel matrices

Abstract The Bruhat decomposition of the space of n × n Hankel matrices is derived from the Bruhat decomposition of the general linear group. Some new results concerning the Hankel minors map H → (det H1,…,det Hn) are obtained (det Hi denotes the i-th principal minor of H). The adherence order of the Bruhat decomposition is determined in the complex case.

Robust adaptive stabilization by high gain feedback and switching

Abstract A wide class of stabilizing adaptive control rules is investigated. The feedback laws combine high gain adaptive procedures with switching functions and stabilize the systems without knowledge of the sign of the high frequency gain. Furthermore, some non-linear structural perturbations are tolerated.