On hybrid state-feedback loops based on a dwell-time logic

In this paper, we extend some results of Prieur et al. (NOLCOS 2010) by adding a dwell-time logic. The idea is to augment a pre-existing (not necessarily stabilizing) continuous-time controller by resetting its state in suitable regions when flow conditions, based on suitable Lyapunov-like functions and a dwell-time logic, are not satisfied. The additional flexibility due to the dwell time allows us to establish global exponential stability of the origin and guarantees some robustness properties. Moreover the solutions of the corresponding hybrid closed-loop systems can be made arbitrarily close to the ones in Prieur et al. (NOLCOS 2010) and therefore the optimal techniques for the maximization of the decay rate or for the overshoot reduction hold.