Sensitivity minimization in active networks by port compensation

This paper extends the notion of sensitivity of feedback systems defined by Bode to interconnected linear multiport active networks. In feedback theory the sensitivity function of the feedback system is a measure of gain and phase as a function of frequency linking variations between closed loop and open loop system. In this paper an analogous sensitivity function is defined for port interconnected networks which is a multiplier between variations in a network's variable with and without interconnection of compensation at the ports. Like in feedback theory this paper shows that the sensitivity function of the compensated multiport network has an affine parametrization in terms of stable network functions. This opens up a way to optimize the sensitivity function for multiport networks analogous to optimization in feedback theory well known as Hα optimal feedback design. An illustrative sensitivity minimization problem is also demonstrated.