On proper and stable stabilising controllers for a class of linear multivariable systems

Abstract

In this paper, we examine the problems of existence and computation of proper and stable stabilising compensators in the feedback path of a special class of linear time-invariant multivariable systems characterised by a strictly proper transfer function matrix. For the class of systems that are ‘square’, i.e. have the same number of inputs and outputs and have no zeros in the closed right half complex plane and the class of ‘non-square’ systems that include a ‘square’ subsystem that has no zeros in the closed right half complex plane we present a sufficient condition for the existence and computation of proper stabilising (pole placing) compensators which in certain cases that depend on the transfer function matrix of the system can be chosen to be stable.