Stability of reset control systems with variable reset: Application to PI+CI compensation

Reset compensation has been used to overcome limitations of LTI compensation. However, since a reset compensator may destabilize a stable base LTI system, stability needs to be guaranteed for a proper application of reset control. The goal of this work is the study of the stability of a nonlinear/hybrid compensator previously developed by some of the authors, referred to as the PI+CI compensator. It is a type of reset compensator with a special structure, in particular a variable reset of the compensator state is performed. In previous work about reset control systems, most of the relevant stability results are restricted to reset compensator with fixed reset, that is compensator states to be reset are always set to zero. In this work, some more general hybrid systems stability work will be adapted to approach stability of reset systems with variable reset, specially focused to the PI+CI compensator. To this end, stability constrained conditions using Lyapunov techniques will be given as several linear matrix inequalities (LMIs). Furthermore, the S-procedure technique will be applied on these constrained LMIs to demonstrate the exponential stability of a PI+CI-based reset control system.