Multivariable system design by transfer function synthesis

Abstract

This paper is concerned with the problem of designing a constant output feedback matrix to synthesize the denominator and certain numerator polynomials of the transfer function matrix of a linear multivariable system. The problem is tackled by first using the special case of unity rank feedback and then removing this restriction to cover the case of unconstrained feedback. Simple expressions relating closed-loop and open-loop transfer functions of multi-variable systems and unity rank feedback are first established. These are then used to develop a recursive synthesis algorithm employing unity rank output feedback. The algorithm uses the pseudo-inverse concept for obtaining least-squares solutions of sots of simultaneous linear equations. The extension from unity rank feedback to unrestricted rank feedback is carried out by considering the feedback matrix as a sum of unity rank matrices. Using this concept and the expressions derived earlier for unity rank feedback, a recursive algorithm is developed for ...