Logarithmic integrals, interpolation bounds, and performancelimitations in MIMO feedback systems
Jie Chen
Automatic Control, IEEE Transactions on
Volume 45, Issue 6, Jun 2000 Page(s):1098 - 1115
Digital Object Identifier 10.1109/9.863595
Summary:We study performance limitation issues found in linear
multivariable feedback systems. Our main contributions include Bode and
Poisson type integral inequalities and performance limits for the
sensitivity and complementary sensitivity functions. These results
characterize and quantify explicitly how open-loop unstable poles and
nonminimum phase zeros may impose inherent limitations on feedback
design and fundamental limits on the best achievable performance. The
role of time delay is also studied in this context. Most notably, we
show that the performance and design limitations in multivariable
systems intrinsically depend on the locations as well as directions of
unstable poles and nonminimum phase zeros, and in particular, on how
pole and zero directions are aligned. The latter is characterized by
angles measuring the mutual orientation between zero and pole
directions, and it is shown to play a crucial role in multivariable
system design
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