Abstract
This paper examines the limitations imposed by Right Half Plane (Rhp) zeros and poles in multivariable feedback systems. The main result is to provide lower bounds on || WXV(s) || <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> where X is S, S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</inf> , T or T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</inf> (sensitivity and complementary sensitivity). Previously derived lower bounds on the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -norm of S and T are thus generalized to the case with matrix-valued weights, including bounds for reference tracking and disturbance rejection. Furthermore, new bounds which quantify the minimum input usage for stabilization in the presence of measurement noise and disturbances are derived.
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