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 im - plementation of a discrete filter, and a comparison is given to other possible realizations.