The Bounded Real Lemma for Internally Positive Systems and H-Infinity Structured Static State Feedback 论文

摘要

We consider the bounded real lemma for internally positive linear time-invariant systems. We show that the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty}$</tex> </formula> norm of such systems can be evaluated by checking the existence of a certain diagonal quadratic storage function. Taking advantage of this fact, the problem of designing a structured static state feedback controller achieving internal stability, contractiveness, and internal positivity in closed loop becomes convex and tractable.