When Is a Linear Continuous-time System Easy or Hard to Control in Practice?

This paper is focused on characterization of easily controllable plants in practical control applications rather than to design an optimal or a robust controller for a give plant. After explaining the background and the motivation of the research topic, we first provide two notions, namely finite frequency positive realness (FFPR) and Condition (π), which represent desirable phase/gain properties for easily controllable plants. We then show closed-form analytical expressions of best achievable \( {\cal H}_2 \) tracking and regulation performances, and we provide the connection between Condition (π) and the achievable robust performance based on \( {\cal H}_\infty \) loop shaping design procedure.