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Generation of sensitivity functions for linear systems using low-order models

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2 Author(s)
Wilkie, Dennis F. ; Ford Motor Company, Dearborn, Mich ; Perkins, William R.

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 onenth-order sensitivity model all the sensitivity functionsfrac{partialx_{i}}{partialv_{j}}|_v^{0}, i=1,...,n, j=1,...,r,for a single-input linear time-invariant controllablenth-order system which depends onrdifferent parameters is reviewed. This method represents an improvement over known methods for generating the sensitivity functions, which generally require a composite dynamic system of ordern(r+1). This result is then extended to the case of multi-input normal linear systems, where, at most,2m-1dynamicnth-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 (mis the dimension ofu). It is shown that the algebraic calculations that must be made in them-input case are much less thanmtimes the calculations needed for the single-input case. The implications of these results for the computer aided sensitivity analysis of systems are discussed.

Published in:

Automatic Control, IEEE Transactions on  (Volume:14 ,  Issue: 2 )