This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn this paper the following problem is considered: Given two co-prime polynomials, find the smallest perturbation in the magnitude of their coefficients, such that the perturbed polynomials have a common root. It is shown that the problem is equivalent to the calculation of the structured singular value of a matrix arising in robust control and a numerical solution to the problem is developed.A simple numerical example illustrates the effectiveness of the method for two polynomials of low degree. Finally, problems involving the calculation of the approximate greatest common divisor (GCD) of univariate polynomials are considered, by proposing a generalization of the definition of the structured singular value involving additional rank constraints.Keywords: Approximate common root of polynomials, approximate GCD, Sylvester resultant matrix, structured singular value, distance to singularity, structured approximations.

Cycling is an increasingly popular mode of travel in cities, but its poor safety record currently acts as a hurdle to its wider adoption as a real alternative to the private car. A particular source of hazard appears to originate from the interaction of cyclists with motorised traffic at low speeds in urban areas. But while technological advances in recent years have resulted in numerous attempts at systems for preventing cyclist-vehicle collisions, these have generally encountered the challenge of accurate cyclist localisation. This paper addresses this challenge by introducing an innovative bicycle localisation algorithm, which is derived from the geometrical relationships and kinematics of bicycles. The algorithm relies on the measurement of a set of kinematic variables (such as yaw, roll and steering angles) through low-cost on-board sensors. It then employs a set of Kalman filters to predict-correct the direction and position of the bicycle and fuse the measurements in order to improve positioning accuracy. The capabilities of the algorithm are then demonstrated through a real-world field experiment using an instrumented bicycle, called "iBike", in an urban environment. The results show that the proposed fusion achieves considerably lower positioning errors than would be achieved based on dead-reckoning alone, which makes the algorithm a credible basis for the development of future collision warning and avoidance systems.

The McMillan degree of a transfer function model is one of the most important structural characteristics of a system. In this paper the problem of identifying the generic McMillan degree of a rational matrix is considered. The transfer function matrices of interest are those referred to as Structured Transfer Function (STF) matrices and have certain elements fixed to zero, some elements being constant and other elements expressing some identified dominant dynamics of the system. For the family of STF matrices the problem of determining the generic McMillan degree is considered using genericity arguments and an optimisation procedure based on path properties of nonnegative integer matrices. A novel approach is introduced that exploits the structure of integer matrices and this leads to an efficient new algorithm for computation of the generic value of the McMillan degree. Links are made to standard problems of optimisation and in particular to the optimal assignment problem. The problem examined here belongs to the general area of Structural Identification where the evaluation of structural characteristics of STF models is under investigation with robust computational methods. Such problems are of interest to large scale system studies.

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