The equivalence of time and frequency-domain multivariable optimal systems

Abstract

The equivalence of multivariable optimal systems designed in time-domain and frequency-domain is derived. Besides the equivalence of input signal and closed-loop transfer function matrix, the equivalence of loop-gain transfer function matrix is also described, such that multivariable optimal systems designed in both time- as well as frequency-domains also satisfy the return difference equality, i.e. both approaches have the same stability margins. In ensuing discussion, the plants employed for both time-domain and frequency-domain optimal systems are shown to be consistent, which have to contain minimum-phase zeros but can be stable or unstable.