Synthesis of continuous-time linear reset feedback system with L2 stability

In this paper, the feedback synthesis of continuous-time linear reset system is considered. The author shows a sufficient LMI condition for the L₂ stability of the reset system with temporal regularization. This result is from the recent Lyapunov type approach by Nesic et al. Then the simultaneous synthesis of reset condition and continuous-time gain feedback via common quadratic Lyapunov function approach is discussed. To obtain the tractable conditions for the synthesis, the jump matrix for reset feedback is fixed a priori. Finally, the stabilizing pair of the continuous-time feedback gain and the flow/jump condition are simultaneously determined via LMI approach.