From Data to Reduced-order Models via Generalized Balanced Truncation

This paper proposes a data-driven model reduction approach on the basis of noisy data with known noise model. Firstly, concept is introduced. In particular, we show that set reduced-order models obtained by applying Petrov-Galerkin projection to all systems explaining characterized in large-dimensional quadratic matrix inequality (QMI) can again be lower-dimensional QMI. Next, develop generalized balanced truncation method relies two steps. First, provide necessary and sufficient conditions such have common Gramians. Second, these Gramians are used construct matrices allow characterize class via terms QMI concept. Additionally, present alternative procedures compute priori posteriori upper bounds respect true system generating data. Finally, proposed techniques illustrated means application an example cart double-pendulum.