Design of High Gain Feedback System with Robust Stability

This paper discusses the problem of designing high gain feedback systems with robust stability. Concerned with disturbance attenuation and/ or transient response, it is known that a high gain feedback control is of great worth. However, to make a high gain feedback scheme more reliable, it is important to consider the robust stability problem against plant perturbation. In this paper we suppose that the feedback system has a nonlinear feedback gain k(y)/y•†1 as a high gain element, and has the SISO plant with uncertainty of the class of M(p0,r) ={p:p=(1+l)p0,•bl(jƒÖ)•b•...•br(jƒÖ)•b,•ÍƒÖ• ̧R,l does not change the number of unstable poles}, where p0 and l denote the nominal plant and perturbation, respectively, and are proper real rational functions. We call a triple (p0,c,r) is robustly positive real if pc/(1+pc) is stable and positive real for all plant in M(p0,r). It is obvious, from