Sensitivity in Dynamical System Analysis†

Abstract

Abstract A few of several possible sets of system condition numbers or sensitivity coefficients are defined relating small changes in system parameters to such measures of system performance as state variables, eigensystems and state variable fuiictionals. Sensitivity functionals are defined also for use in cases where anticipated but undesirable system perturbations occur. The linear or approximately linear dynamical system is of special interest and for these systems it is shown that the condition numbers of all eigenvalues with respect to all elements of the n × n system matrix A are expressible by n 1-term dyads of the form v i X i T, the reciprocal vectors and eigenvectors of A respectively. These matrices are particularly useful in design processes based upon eigenvalue configurations, and it is shown also how they may be employed in the evaluation of a particular class of time weighted functional of the form a of free, stationary, linear systems. Finally it is noted how these matrices are modified ...