Synthesis of optimal constant-gain positive-real controllers for passive systems

This paper presents synthesis methods for the design of constant-gain positive real controllers for passive systems. The results presented, in conjunction with the work by Kelkar et al. (1997, 1998) on passification of non-passive systems, offer a useful synthesis tool for the design of passivity-based robust controllers for non-passive systems as well. Two synthesis approaches are given for minimizing an LQ-type performance index, resulting in optimal controller gains. Two separate algorithms, one for each of these approaches, are given. The synthesis techniques are demonstrated using two numerical examples: control of a flexible structure and longitudinal control of a fighter aircraft