Generalized quadratic weights for asymptotic regulator properties

Abstract

This paper describes a generalized quadratic weight selection procedure based on asymptotic modal properties of linear-quadratic regulators as control weights tend to zero. Explicit formulas are developed for weighting matrices which produce an asymptotic eigenstructure consisting of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p \leq n-m</tex> finite modes, with the rest tending to infinity in selectable Butterworth patterns or determined by other secondary design considerations.