Application of matrix methods to the linear least squares synthesis of multivariable systems

✍ Scribed by R.C. Amara

• Publisher: Elsevier Science
• Year: 1959
• Tongue: English
• Weight: 704 KB
• Volume: 268
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(59)90352-7

✦ Synopsis

The class of systems treated in this paper is that characterized by a multiplicity of inputs and outputs. For such linear multivariable systems subject to continuous stochastic inputs with arbitrary self-and cross-correlations, a derivation is made of the equations to be satisfied by the optimum transfer-fuuction matrix. The criterion of performance which is used is the minimization of the sum of the mean-square errors between the set of actual outputs and a set of desired outputs.

The analysis divides the nmltivariable problem into two principal parts. I11 the first, designated the filter case, are included those systems in which the only restriction on the linear transfer-function matrix to be realized is that of physical realizability. Included in the second, the control case, are those systems in which a controlled matrix or plant is specified which imposes additional restrictions on the over-all performance of the system.

The results of the analysis are presented compactly in matrix form. For signal power spectra and plant matrices satisfying prescribed conditions, explicit matrix solutions to the minimization equations are obtained.