The Letov Formula for Bounded Real Systems

Abstract

The Letov formula allows the computation of closed-loop poles in the classical linear quadratic regulator context. In this paper, a similar formula is proposed to compute, directly from the transfer function of a bounded real system, the closed-loop poles of the system under a suitable performance index. Moreover, the presented result allows both to directly verify whether an asymptotically stable system is BR and, if not, to compute its ℋ∞ norm.