Exponential stability of a PI plus reset integrator controller by a   sampled-data system approach
  The paper deals with the stability analysis of time-delay reset control systems, for which the resetting law is assumed to satisfy a time-dependent condition. A stability analysis of the closed-loop system is performed based on an appropriate sampled-data system. New linear matrix inequality (LMI) conditions are proposed to ensure the exponential stability of the closed-loop resulting of the connection of a plant with a proportional and integral controller together with a reset integrator (PI+RI). 
M. A. Dav\'o, F. Gouaisbaut, A. Ba\~nos, S. Tarbouriech, A. Seuret
cs.SY