مرکز منطقه ای اطلاع رساني علوم و فناوري - Generation of a Class of Equivalent Networks and its Sensitivities

Abstract :

This paper presents a method of generating a class of equivalent networks from an initial network $\\eta^{(0)}$ such that a transfer function $H(p)$ kept invariant throughout the transformation. The class of networks to be considered is chosen so that the sensitivities of $H(p)$ to changes in the network elements of the initial network given by $S_{e_{k}}H(p)= frac{\\partial H (p)}{\\partial e_{k}}frac{e_{k}}{H(p)}$ and the sensitivities of all of the generated equivalent networks can be obtained by simple matrix multiplication. Partial differentiation is avoided. The equivalent networks are generated from $\\eta^{(0)}$ by transforming the vector of network variables and the input vector in the equilibrium equations defined below. The transformation is performed in such a manner that the equivalent networks $\\eta^{(1)}$ are generated by congruence, transforming the matrices $M$ and $N$ that appear in the system of equations $M \\dot{x} = -Nx + bu_{\\in}$ $w = d^{t}x$ . The single-output transfer function $H(p)$ is given by $d^{t} (pM + N)^{-1} b$ . Provided that the equations possess specified properties, the sensitivities are easily obtained and can be applied to the problem of sensitivity minimization. Furthermore, if $\\phi$ is the sum $\\sum |S_{e_{k}}|^{2}$ , then the partial derivatives of $\\phi$ with respect to the transformation parameters are readily obtained. Again only matrix multiplication is required.