Stability and Performance of SISO Control Systems With First-Order Reset Elements
We consider set-point regulation and robust sta- bility properties of a class of reset control systems consisting of a minimum-phase relative degree-one linear SISO plant controlled by a novel first-order reset element (FORE). These results rely on necessary and sufficient conditions for exponential and finite gain stabilityof a classof planar reset systems consistingof a scalar linear plant controlled by the novel FORE. We show that the gain of the planar reset system decreases to zero as the pole and/or the gain of the FORE are increased to infinity. A number of sta- bility results, including Lyapunov conditions for and exponen- tial stability, for a larger class of reset and hybrid systems are pre- sented and used to prove our main results. Index Terms—First-order reset element (FORE), homogeneus hybrid systems, temporal regularization.