Data-driven analysis and design beyond common Lyapunov functions

In this paper we investigate data-based analysis and design problems without making the prevailing assumption that there exists a common Lyapunov function for all systems unfalsified by data. In particular, we provide necessary and sufficient conditions under which a given set of state data are informative for stability, in the sense that all systems explaining the data are stable. These conditions are derived by making use of the celebrated Kalman-Yakubovich-Popov lemma. We also explain the potential of extending these results to other analysis problems like data-based stabilizability, and to the design of stabilizing controllers. The results are applied to analyze the stability of a large-scale network, which highlights the tractability of the provided framework in comparison to previous conditions involving linear matrix inequalities.