Nonlinear Programming and Multiparameter Sensitivity in Linear Time-invariant Networks

A computational solution is obtained to the multiparameter sensitivity problem for linear time-invarient networks in which large element variations are permitted. The various definitions of multiparameter sensitivity are critically reviewed and it is concluded that a definition which was proposed by Hakimi and Cruz is currently the most general since the other definitions are valid only for small variations in the network element values. Their definition of multiparameter sensitivity is extended to a measure over a band of frequencies and to such cases as n-port networks where it is desirable to consider more than one transfer function. A method is presented for the selection of the temperature coefficients of active-RLC networks to reduce multiparameter sensitivity. A second-order approximation to the network function variation is studied by considering the first three terms of a Taylor series expansion. A Mikulski-Ur type of correlation is obtained between the third Taylor series term and the classical root sensitivities. Also the first three Taylor series terms are related to the k-trees which Hakimi and Green defined. Blostein's results relating the sum of classical Bode sensitivity functions to the first derivative with respect to complex frequency is extended to the second derivative and n-th derivative cases. (Author).