Synthesis of output feedback linear reset control based on common quadratic Lyapunov-like function

Continuous-time reset control is a hybrid feedback control of a continuous-time controller and a state dependent reset rule. In this paper, a synthesis of the purely output-feedback linear reset control is considered via LMI approach. The reset control consists of the continuous-time controller and the reset law determined by jump and reset matrices. Different from the state-feedback case in the author´s previous result, not only the controller but the reset law should depend on the measured output and the controller state only. This can be done by introducing the characteristic structure into the jump and reset matrices. The sufficient condition for the existence of ℒ₂ stabilizing output-feedback reset control is also discussed.