Analyse de stabilité des systèmes avec réinitialisation en présence d'incertitudes

This paper is dedicated to the study of specific hybrid systems: reset control systems. A reset system is a system whose states are reset whenever its output and input satisfy an appropriate relationship. Stability analysis and L2-performance are studied for systems (and in particular for systems in closed-loop with reset controller) in presence of perturbations and parametric uncertainties. Based on the use of quadratic and piecewise quadratic Lyapunov functions, constructive conditions into LMI form are proposed. The potentialities of the approach are illustrated on a numerical example borrowed from the literature.