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3 International Journal of Applied Mathematics and Computer Science

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On hyper-regularity and unimodularity of Ore polynomial matrices

Fritzsche K., Röbenack K.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 3

583--594

We investigate Ore polynomial matrices, i. e., matrices with polynomial entries in d/dt whose coefficients are meromorphic functions in t and as such constitute a non-commutative ring. In particular, we study the properties of hyper-regularity and unimodularity of such matrices and derive conditions which make it possible to efficiently check for these characteristics. In addition, this approach enables computation of hyper-regular left and right and unimodular inverses.

On generalized inverses of singular matrix pencils

Röbenack K., Reinschke K.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 1

161-172

Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate singular matrix pencils. The relations between the Kronecker structure of a singular matrix pencil and the multiplicity of poles at zero of the Moore-Penrose inverse and the Drazin inverse of the rational matrix are investigated. We present example networks whose circuit equations yield singular matrix pencils.

Observer design using a partial nonlinear observer canonical form

Röbenack K., Lynch A. F.

International Journal of Applied Mathematics and Computer Science

2006

Vol. 16, no 3

333-343

This paper proposes two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form (POCF). Observability and integrability existence conditions for the new POCF are weaker than the well-established nonlinear observer canonical form (OCF), which achieves exact error linearization. The proposed observers provide the global asymptotic stability of error dynamics assuming that a global Lipschitz and detectability-like condition holds. Examples illustrate the advantages of the approach relative to the existing nonlinear observer design methods. The advantages of the proposed method include a relatively simple design procedure which can be broadly applied.