Reduced-order robust controllers: H/sub infinity /-balanced truncation and optimal projection

Abstract

Some insights are given regarding the H/sub infinity /-balanced truncation and optimal projection methods for reduced-order robust control. After a concise description of the optimal projection approach, it is shown how positive semidefiniteness of the Lagrange multiplier implies a minimized, not just extremized, auxiliary cost. When the results are specialized to the full-order case, it is observed that the apparently redundant fourth optimal projection equation has an important role to play, both in guaranteeing a minimized (not just extremized) auxiliary cost, and in removing nonminimal controller states. >