Using Luenberger observers and dwell-time logic for feedback hybrid loops in continuous-time control systems

For linear control systems, we add a Luenberger observer to extend the state feedback hybrid loop designs of (Prieur et al., NOLCOS 2010) and (Fichera et al., ADHS 2012), to the output feedback case. This defines an output feedback controller. The hybrid loop consists in a continuous-time dynamics when the estimate of the state leads to a non-increase of a suitable Lyapunov-like function, and in a jump equation when this condition is not satisfied. The jump equation is defined by means of a static state feedback law from the observed state. Four techniques based on different reset maps and flow and jump sets are proposed, all of them exploiting a suitable dwell-time logic. For the proposed designs we prove global exponential stability of the origin. The effectiveness of the proposed solutions is illustrated by simulation examples where we show suitable reduction of the output overshoot.