Delay-dependent stability of reset control systems with anticipative reset conditions

Abstract Typical reset conditions can be the zero crossing of the tracking error signal e ( t ) = 0 or when input and output of the reset controller have opposite signs e T ( t ) u ( t ) ≤ 0. This paper studies the delay-dependent stability properties for delayed systems with state-dependent reset impulses when anticipation reset actions are used on the reset event conditions. The analysis includes the application of a Lyapunov-Krasovskii functional technique in the time domain for dealing with stability conditions and a frequency domain approach. The effectiveness and the drawback of such an approach are illustrated on an example.