Stability of time-delay reset control systems with time-dependent resetting law*

This work presents results on the stability of time-delay reset control systems under time-dependent resetting conditions. The stability of a reset control system composed by a time-delay process and a proportional and integrative plus Clegg integrator (PI+CI) compensator is tackled by using the framework of sampled-data systems. It leads to sufficient stability conditions expressed in terms of LMIs (Linear Matrix Inequality), that depend explicitly on the reset times. In contrast to previous results, the proposed conditions allow to guarantee the stability of reset systems with unstable base system.