Scaled graphs for reset control system analysis

Scaled graphs allow for graphical analysis of nonlinear systems, but are generally difficult to compute. The aim of this paper is to develop a method for approximating the scaled graph of reset controllers. A key ingredient in our approach is the generalized Kalman–Yakubovich–Popov lemma to determine input specific input–output properties of a reset controller in the time domain. By combining the obtained time domain properties to cover the full input space, an over-approximation of the scaled graph is constructed. Using this approximation, we establish a feedback interconnection result and provide connections to classical input–output analysis frameworks. Several examples show the relevance of the results for the analysis and design of reset control systems.