  In this paper, three laws are obtained for multiple-input multiple-output
feedback systems, which are in entropy domain, frequency domain, and time
domain, respectively. The system setup is that with causal plants and causal
controllers. Those laws characterize the performance limitations of such
systems imposed by the feedback mechanism. Some new notions are proposed to
facilitate the analysis: negentropy rate, extended spectral flatness (extended
Wiener entropy), Gaussianity-whiteness measure (joint Shannon-Wiener entropy),
etc. Two approaches are adopted: the integrated approach and the divided
approach. And 'uncertainty principles' are found in minimum variance control.
Besides, performance limitations in minimum variance estimation and filtering
are obtained. In the end, the special case of linear time-invariant feedback
systems is discussed.
