GENERATION OF SENSITIVITY FUNCTIONS FOR LINEAR SYSTEMS USING LOW-ORDER MODELS

New proofs are given for the recently demonstrated total symmetry and complete simultaneity properties for the companion canonic form for single-input linear time-invariant controllable systems. These proofs result in a convenient closed-form expression for the complete simultaneity property. The use of these properties to generate by one nth-order sensitivity model all the sensitivity functions for a single-input linear time-invariant controllable nth-order system which depends on r different parameters is reviewed. This method represents an improvement over known methods for generating the sensitivity functions, which generally require a composite dynamic system of order n(r+1). This result is then extended to the case of multi-input normal linear systems, where, at most, 2m-1 dynamic nth-order systems are needed in addition to the system to generate all the sensitivity functions of the system state with respect to any number of parameters (m is the dimension of u). It is shown that the algebraic calculations that must be made in the m-input case arn much less than m times the calculations needed for the single-input case. The implications of these results for the computer aided sensitivity analysis of systems are discussed. Copyright © 1969 by The Institute of Electrical and Electronics Engineers, Inc.