  This paper formulates and solves the problem of robust compensation of
multiport active network. This is an important engineering problem as networks
designed differ in parameter values due to tolerance during manufacture from
their actual realizations in chips and hardware. Parameters also undergo
changes due to environmental factors. Hence, practical use of networks requires
compensation which is only possible by connecting compensating network at the
ports. The resulting interconnection is then required to be stable over a range
of parameter values. This is called robust compensation. This paper formulates
such a problem using an extension of the coprime factorization theory well
known in feedback control theory to the situation of multiport network
interconnection developed in \cite{msm1} and formulates the robust
stabilization problem as an $H_{\infty}$ optimization problem. The port
interconnection of networks does not confirm with computation of the function
of the interconnected network analogous to that of the feedback interconnection
using signal flow graph. Hence the well known stabilization and stability
theory of feedback systems cannot be utilized for such a problem. A new
formulation of stabilization theory of network interconnection was formulated
and developed by the authors in \cite{msm1}. The variations of parameters of
the network are used to define a worst case neighborhood of the network in
terms of its coprime fractions at the nominal values of parameters. The
solution of the optimization problem is then carried out by the standard
procedure of converting such a problem to the Nehari optimization problem
\cite{fran}. This methodology of solving the robust compensation of multiport
networks using feedback control theory is believed to be novel.
