Sensitivity reduction in multivariable systems

Feedback is used to decrease the sensitivity of a system to plant uncertainty or to disturbances. This thesis is focused on the reduction of sensitivity to additive disturbances applied at the output. Systems are represented by linear multivariable frequency responses whose inputs and outputs belong to(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)Rigorous conditions under which feedback can reduce sensitivity are derived.It is shown that given a minimum phase single input-single output plant, there exists a feedback compensator which reduces sensitivity below any arbitrarily positive value on any finite frequency interval while not exceeding a specified upper bound in the right half complex plane.It is also shown that given a multivariable invertible plant which approaches diagonal dominance at high frequencies, it is possible to build a diagonal feedback compensator to reduce the sensitivity below any arbitrarily value on any finite frequency interval while not exceeding a specified upper bound in the right half complex plane.A relationship between sensitivity reduction and decentralized control is established. It is shown that reducing sensitivity to additive disturbances at the outputs is in essence the same as achieving local control of a multivariable system