Multidimensional Systems Design: Novel Directions

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When a model of a one-dimensional (1-D) system is known precisely, many properties of interest, e.g. stability, can be investigated through the analysis of a set of polynomials in one independent variable. A difficulty in such an analysis is that the set of polynomials may be infinite and the question arises of how to reduce the study of this infinite set to the study of a finite set of low order. Furthermore, the coefficients appearing in the set of polynomials are generally not known precisely and only bounds on the coefficients can be given. This brings up the question of the robustness of the properties of interest to parameter variations. For 1-D systems, these two questions have been reasonably well resolved. The goal of this research is to generalize certain results regarding the above questions for 1-D systems to two- or three-dimensional systems. Such systems are important in a number of engineering applications such as optical image processing and robotics. In particular, the two general research tasks are property invariance of n-dimensional polynomials under coefficient perturbations, and polynomial irreducibility and a type of spectral factorization.