Stability analysis for reset systems with input saturation

This paper is devoted to the stability analysis for a class of reset systems, such as those including a Clegg integrator or a FORE (first order reset element). The system under consideration is subject to input saturation. Hence, constructive conditions, allowing to characterize the region of stability of the saturated closed-loop system, are proposed based on the use of some suitable Lyapunov functions and a modified sector condition. LMI-based optimization schemes for maximizing the size of the region of stability are then derived. In presence of an additive disturbance, the problem of L₂ stability is also addressed.