Informativity of Data-Knowledge Pairs for Lyapunov Equations
In the past few years, data informativity with prior knowledge has attracted increasing attention. This line of research aims to characterize whether data and prior knowledge suffice for system analysis or design. In this paper, we investigate such a characterization for the data-driven problem of determining a unique solution to Lyapunov equations. First, we introduce a notion of joint informativity for data-knowledge pairs as an extension of the standard informativity concept. Second, we derive an algebraic necessary and sufficient condition for the joint informativity. Finally, we provide further insights into the joint informativity by considering a special case of prior knowledge. The characterization presented in this paper is developed for a wide class of prior knowledge, enabling the incorporation of various forms of system information.