Robust Control Based on Dissipativeness of Open-Loop Systems

Abstract

This paper proposes a robust control design method by imposing dissipativeness on open-loop systems. First, it is shown that stability of nominal feedback systems is equivalent to dissipativeness of open-loop systems. This result justifies imposing dissipativeness on open-loop systems. Second, a robust stability for some class of complex perturbations guaranteed by dissipativeness of open-loop systems is shown. This explains that our method is effective for ensuring gain and phase margins of feedback systems. Third, it is shown that dissipativeness of open-loop systems is equivalent to bounded realness of certain closed-loop transfer functions. This fact implies that H∞ control which evaluates only gain property possesses the ability to take into consideration both gain and phase properties of open-loop transfer functions, as well as it gives a controller design method based on dissipativeness of open-loop systems.