THE CALCULATION OF FUNCTIONALS OF THE TIME AND FREQUENCY RESPONSE OF A LINEAR CONSTANT COEFFICIENT DYNAMICAL SYSTEM

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Abstract
For a linear, constant coefficient dynamical system whose state space behaviour is governed by the matrix equation x= Ax, a matrix B is defined which is formed from A in a simple manner. It is shown that the inverses of B and its powers may be used to calculate a large class of functionals of the time and frequency responses of the system directly in terms of the system parameters. The results should be useful in the synthesis of dynamical systems.