Application of a Bilinear Theorem to Network Sensitivity

The Invariance Properties of a Multivalue n-Port in a Linear Embedding

“…An equivalent representation for a two-value n-port network which can be applied in conjunction with the forms (7) and (9) is Z1 = exp (-j arctan v%) z2 = z1* (13) where L is the diagonal -matrix of the eigenvalues of (7) or (9). In conjunction with the invariant (11) and (12), we take the function arcsin in place of arctan in (13).…”

“…In conjunction with the invariant (11) and (12), we take the function arcsin in place of arctan in (13). For sake of completeness, we may add that in connection with a reciprocal embedding the transformation T1 …”

One‐dimensional orthogonal search—a method for a segment approximation to acceptability regions

“…In the above x ( ui) -x, can be substituted, using (2), to obtain a final biquadratic formula for the square of the magnitude:…”

Sensitivity: Old Questions, Some New Answers

“…In a recent paper Kuh [32] has related general feedba k theory and the state space representation l of linear time in ariant systems. When x is a circuit immittance a useful alternate to Bode's formulation for computational purposes is available based upon the following bilinear formulation as discussed by Parker, Peskin, and Chirlian [3] :…”

“…Equation (1) may be viewed as a three-port generalization of Thevenin's theorem. As discussed in [3] and illustrated by a typical example in Fig. 1, when x is an impedance element (x = z) it is possible to express variations of the voltageto-voltage transfer function, T(s, z) = E,(s)/E,(s), as A W, 4 _ T(s, 00) -T(s, 4 AZ z33 + z + AZ (2) Equation (2) is an exact expression involving finite (large) variations of Az and reduces to (3) for incremental variations as AZ approaches zero.…”