Stability properties for a class of reset systems, such as systems containing a Clegg integrator, are investigated. We present Lyapunov based results for verifying L-2 and exponential stability of reset systems. Our results generalize the available results ill the literature and can be easily modified to cover L-p stability for arbitrary p epsilon [1, infinity]. Several examples illustrate that introducing resets in a linear system may reduce the L-2 gain if the reset controller parameters are carefully fluted. (C) 2008 Elsevier Ltd. All rights reserved.