Complete decoupling of linear multivariable systems by means of linear static and differential state feedback

The concept of complete decoupling is introduced in this paper. We show in particular that for any linear controllable system with non-singular transfer matrix, there always exists a static and differential state feedback such that the closed-loop system is completely decoupled.     

Comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models

The estimation of the parameters of a transfer function model is considered. Relationships between the total least squares (TLS) and instrumental variable (IV) approaches are outlined. Both methods are able to compute strongly consistent parameter estimates. TLS can be considered as a variation on the IV method where the IV are functions of the time instant and the estimated model parameters. TLS computes strongly consistent estimates of the true model parameters if the outputs and possibly the inputs are independently disturbed by discrete, stationary white noise with zero mean and equal variance. The IV need not be generated. Hence TLS is much simpler to use but more restrictive (IV allows arbitrary noise models) and computationally not so attractive. Next, simulation results are presented comparing the short sample accuracy properties of both methods. When the outputs and possibly the inputs are disturbed by stationary zero mean while noise, TLS outperforms the ordinary IV methods. The accuracy becomes comparable by extending the IV sufficiently. The superiority of TLS is particularly clear in cases where the zeros of the polynomial operating on the outputs are close to the unit circle or where both the inputs and outputs are noisy.     

Novel theory for polynomial and rational matrices at infinity. Part1. Polynomial matrices

A new approach for dealing with the structural properties of polynomial and rational matrices at infinity is presented. In this first part of the development, the attention is focused on polynomial matrices. Some fundamental notions and definitions such as the notion of homogeneous form for polynomial matrices are introduced. These enable us to define important concepts such as the cancellation at infinity, coprimeness at infinity, etc. for polynomial matrices in precisely the same way as for their finite counterparts. We demonstrate that our approach allows interesting generalizations of some important conventional concepts.     

QSVD approach to on- and off-line state-space identification

Moonen et al. (1989 a), presented an SVD-based identification scheme for computing state-space models for multivariable linear time-invariant systems. In the present paper, this identification procedure is reformulated making use of the quotient singular value decomposition (QSVD). Here the input-output error co-variance matrix can be taken into account explicitly, thus extending the applicability of the identification scheme to the case were the input and output data are corrupted by coloured noise. It turns out that in practice, due to the use of various pre-filtering techniques (anti-aliasing, etc.), this latter case is most often encountered. The extended identification scheme explicitly compensates for the filter characteristics and the consistency of the identification results follows from the consistency results for the QSVD. The usefulness of this generalization is demonstrated. The development is largely inspired by recent progress in total least-squares solution techniques (Van Huffel 1989) for the identification of static linear relations. The present identification scheme can therefore be viewed as the analogous counterpart for identifying dynamic linear relations.     

Generalized invariant polynomials and the generalized companion form

A precise algebraic basis is constructed for the so-called generalized rational canonical form that was recently introduced by Tan and Vandewalle (1986 a). The development is based on the concept of generalized invariant polynomials. The introduction of the generalized companion form is crucial for the whole theory.     

Early mineralization of matrix vesicles in the epiphyseal growth plate

Matrix vesicles (MVs) induce the primary mineralization in collagen-rich hard tissues such as bone, mineralizing cartilage and dentine. Calcium and phosphate ions accumulate at the inner MV membrane. This accumulation takes place in association with phospholipids alone and/or in association with Annexin V, which displays Ca ion channel activity when inserted in membranes; consequently, Annexin V may be involved in Ca uptake by matrix vesicles. The first crystal nuclei are formed at these macromolecules of the MV inner membrane. They grow to stable nanometre-sized particles, dots, which coalesce to form chains of dots along the macromolecules of the MV inner membrane. At the same time, or shortly afterwards, chains of these Ca phosphate dots also develop inside the MVs. The measured centre-to-centre distances between these dots represent approximately the distances between the nucleating sites, called active sites, along the MV matrix molecules. The mineralization does not stop at the MV membrane but expands continuously into the extravesicular region in radial directions to form nodules. These radiating Ca phosphate chains, which coalesce to form needles, are composed of such primary dots, which have developed at the nucleating sites of the corresponding macromolecules.