Verifying dissipativity properties from noise-corrupted input-state data

There exists a vast amount of literature how dissipativity properties can be exploited to design controllers for stability and performance guarantees for the closed loop. With the rising availability of data, there has therefore been an increasing interest in determining dissipativity properties from data as a means for data-driven systems analysis and control with rigorous guarantees. Most existing approaches, however, consider dissipativity properties that hold only over a finite horizon and mostly only qualitative statements can be made in the presence of noisy data. In this work, we present a novel approach to determine dissipativity of linear time-invariant systems from data where we inherently consider properties that hold over the infinite horizon. Furthermore, we provide rigorous guarantees in the case of noisy state measurements.