Control of linear systems subject to time-domain constraints with polynomial pole placement and LMIs

This note focuses on the control of continuous-time linear systems subject to time-domain constraints (input amplitude limitation, output overshoot) on closed-loop signals. Using recent results on positive polynomials, it is shown that finding a Youla-Kucera polynomial parameter of fixed degree (hence, a controller of fixed order) such that time-domain constraints are satisfied amounts to solving a convex linear matrix inequality (LMI) optimization problem as soon as distinct strictly negative closed-loop poles are assigned by pole placement. Proceeding this way, time-domain constraints are handled by an appropriate choice of the closed-loop zeros.