Research Projects

This research project focuses on the concept of Greatest Common Right Divisors (GCRDs) of several polynomial matrices, which are crucial in various fields of engineering and science, including systems and control theory. The project aims to compute exact or approximate GCRDs of several univariate polynomial matrices, generalizing the concept of computing exact or approximate GCDs of several polynomials. The project will construct a polynomial matrix P(s) by stacking the given polynomial matrices one below the other. The equivalence of the existence of a GCRD of several polynomial matrices with the non-primeness of P(s) and connect it to the rank deficiency of a generalized Sylvester matrix will be demonstrated. Two new algorithms based on Singular Value Decomposition (SVD) and QR decomposition will be presented to compute a GCRD from the generalized Sylvester matrix. The project will also compute approximate GCRDs of several polynomial matrices using Structured Low-Rank Approximation (SLRA) of a certain generalized Sylvester matrix. The applications of exact and approximate GCRDs are not limited to control theory and signal processing but also find their use in the frequency domain approach to multivariable control theory. They play an essential role in the theory and application of general differential systems and linear multivariable feedback system design.