SQUARING UP AND REGULATION IN A CLASS OF LINEAR MULTIVARIABLE SYSTEMS

Non-square linear multivariable systems means that the number of inputs and the number of outputs of these systems are not equal. This type of systems has certain difficulties in many control aspects. Squaring a non-square multivariable system, is done by making the number of inputs equal to the number of output; this is accomplished either by squaring up or by squaring down operations. In this paper the problem of squaring up certain non-square linear multivariable system is solved by finding additional inputs or outputs such that the resulting square system has arbitrarily zero locations. The problem of regulation of this type of multivariable systems is tackled, based on the fact that non-square linear multivariable systems almost always possess no zeros. The zeros introduced by squaring up operations, are located at the position of an equal number of system poles and consisting fixed modes. By using certain output feedback, developed by the parameters of the system, the remaining poles are asymptotically assigned to arbitrary locations and the output response is nearly regulated. The proposed method is simple, efficient and easily programmed using MATLAB to deal with practical large scale systems.