On reset control systems with second-order plants

Reset control has the potential of providing better trade-offs among competing specifications compared to LTI control. We consider a specific class of reset control systems consisting of a feedback interconnection between a linear second-order system and a so-called first-order reset element. Despite the simplicity of this feedback system, few theoretical results are available to quantify stability and performance. The paper develops a necessary and sufficient condition for asymptotic stability and a sufficient condition for BIBO stability. We also characterize steady-state response, overshoot, rise time and settling time to step input.