LMI-Based Reset ${\mathcal H}_{\infty}$ Design for Linear Continuous-Time Plants

In this technical note, an optimization-based synthesis of a multi-objective reset controller for linear plants is presented. The result allows designing via convex tools with a line-search a multi-objective reset controller optimizing both the exponential converging rate and the L
₂
gain. A novel peculiarity of our scheme is that the underlying linear flow dynamics is not necessarily stabilizing. This last property is the consequence of taking into account where the flowing trajectories lay and lead to improved performance, especially in terms of decay rate. Some simulations illustrate the usefulness of our techniques.