Dieter Prätzel-Wolters

Adaptive Tracking for Scalar Minimum Phase Systems

We present the concept of a universal adaptive tracking controller for classes of linear systems. For the class of scalar minimum phase systems of relative degree one, adaptive tracking is shown for reference signals, that are bounded solutions of linear differential equations. The controller requires no identification of the system parameters. Robustness properties are explored.

A balanced canonical form for discrete-time minimal systems using characteristic maps

Abstract This paper presents a balanced canonical form for the class of discrete-time minimal systems. The main tool is to establish a bijection between the set of minimal systems and the class of minimal discrete-time asymptotically stable systems of the same dimension. This characteristic map is shown to preserve system equivalence and balancing. The canonical form for discrete-time minimal systems is then constructed by mapping the system to its discrete-time asymptotically stable counterpart via the characteristic map, transforming the resulting system to Lyapunov-balanced canonical form, and returning to the original system class by means of the inverse characteristic map.

Parameter depending state space descriptions of index-2-matrix polynomials

Abstract To a quadratic matrix polynomial P with coefficients in R n×n , which originated from an electrical network and depending on a parameter vector q∈ R ϱ , a matrix A(q) and a parameter set Ω are assigned such that for all q∈Ω the eigenvalues of A(q) coincide with the zeros of detP(.;q). To find A(q) and the corresponding parameter set Ω two algorithms are proposed where the first one is similar to the Algorithm 3.6 of Van Dooren [Linear Algebra Appl. 27 (1979) 103]. The reason to compute A(q) parameter depending is given by the desire to apply the matrix perturbation theory of Stewart and Sun [Matrix Perturbation Theory (Academic Press, 1990)] to study the influence of q on the zeros of the determinant of P. The assumption that P is derived from the Laplace transform of a DAE system describing an electrical network implies that its coefficients admit representations containing sums of the form ∑vkqkwkT, where vk and wk are the unit vectors or the nonvanishing difference of two such vectors. This circumstance is decisive for the efficiency of our two algorithms.

Dipolynomial minimal bases and linear systems in AR representation

Abstract This paper deals with a module-theoretic approach to the dipolynomial matrix parametrization of discrete-time behavior systems as introduced by Willems. Canonical minimal-lag representations for these behaviors are constructed which are tighter than the corresponding polynomial representations.

Parameter influence on the zeros of network determinants

Abstract To a network N (q) with determinant Δ(s;q) depending on a parameter vector q∈ R ϱ via identification of some of its vertices, a network N (q) is assigned. The paper deals with procedures to find N (q) , such that its determinant Δ (s;q) admits a factorization in the determinants of appropriate subnetworks, and with the estimation of the deviation of the zeros of Δ from the zeros of Δ. To solve the estimation problem state space methods are applied.