A simple division method for multivariable system analysis and design

In the analysis and design of multivariable control systems described by the matrix fraction descriptions (MFDs), it is often required to carry out the division of two polynomial matrices. However, there is a lack of efficient methods for performing this type of division. In this dissertation, a simple division method is developed for solving the Diophantine equations and associated problems, such as the determination of observability(controllability) indices, the irreducible right(left) MFDs from reducible or irreducible left(right) MFDs, and the greatest right(left) common divisor of two polynomial matrices without utilizing the state space realization of the MFDs. Also, the division method is employed to carry out the partial fraction expansion of MFDs with distinct or repeated latent roots. Furthermore, the division method is applied to obtain the irreducible right MFD from the transfer function matrix which may be the multivariable system controller. The design procedures for the realization of this irreducible right MFD without using multiwinding transformers and integrators are then presented. Finally, the division method is utilized to construct the generalized matrix continued-fraction descriptions and to obtain the reduced-degree models from a higher-degree MFD. The newly developed division method greatly reduces the computational efforts of existing methods and provides new view points for the analysis and design of multivariable control systems.