Soft-Reset Control With Max-of-Quadratics Lyapunov Certificates

In this article, we further develop a novel control paradigm encoding the core behavior of a reset control system within a continuous-time feedback, described by a differential inclusion. A tuning knob allows adjusting how close the continuous-time feedback resembles the behavior of the underlying reset controller. The Lyapunov conditions that we derive naturally lead to a sum-of-squares formulation allowing for the design of max-of-quadratics Lyapunov certificates associated with polynomial multipliers. A few application examples confirm the practical effectiveness of the proposed solutions.