APPLICATION OF MATRIX METHODS TO THE OPTIMUM SYNTHESIS OF MULTIVARIABLE SYSTEMS SUBJECT TO CONSTRAINTS

Matrix methods are used to extend well-known concepts in single variable systems to the case of systems with several inputs and outputs. The analysis of such multivariable systems, when subjected to random inputs, is considered in the time and frequency domains. Constraints are set up in terms of bandwidth and saturation - as logical extensions of the single variable case for multivariable systems, and the physical significance of such constraints is discussed. Using the matrix relations obtained, a vector integral equation of the Wiener-Hopf type is derived by minimizing a generalized mean square error. The effect of constraints on the minimization procedure is studied using variational methods. (Author)