Multivariable feedback, sensitivity, and decentralized control

In this paper the problem of sensitivity, reduction by feedback is studied and related to a problem of decentralized control. A plant will be represented by an matrix of frequency responses, which may be unstable or irrational. The object will be to find conditions on under which a diagonal feedback can make the sensitivity arbitrarily small over some specified frequency interval [ ] without violating a global sensitivity, bound , ( some const. >1) for . It will be shown that such a diagonal feedback of the "high gain" type can be constructed whenever is analytic in satisfies an attenuation condition near , and approaches diagonal dominance at high frequencies. It will also be shown that these conditions on the plant can be interpreted as conditions for the existence of a decentralized wide-band control scheme.