Eigenvalue sensitivity and state-variable selection

The first part of this paper presents a new measure of sensitivity specifically applicable to the realization of a linear discrete system on a digital computer. It is also shown that the sensitivity of the eigenvalues to parameter inaccuracies in the realization depends strongly on the choice of state variables. From these considerations, a realization is obtained which is "best" for a large class of systems of interest with regard to minimizing storage requirements, arithmetic operations, parameter accuracy, and eigenvalue sensitivity. The second half of the paper considers the very practical problem of determining the number of bits accuracy required in the computer-stored parameters of the system to achieve satisfactory performance. For the realization found to be a best compromise, equations are obtained for determining these bit requirements. Examples are given showing the application of this realization to the computer implementation of a discrete filter, and a comparison is given to other possible realizations.