Statistical Bounds on Identified QSR Dissipative Properties from Input-Output Data

Dissipativity is a powerful tool in control design as it can be used to ensure closed-loop stability using open-loop input-output properties. This paper presents a framework to estimate the QSR-dissipative parameters of a discrete-time system from estimates of either the power spectral response or transfer function of the system. Specific methods are presented for estimating the input feedforward passivity index, conic sector bounds and
$\mathcal{L}_{2}$
-gain of the system. Methods are also presented to propagate the bound on the worst-case error from the power spectral response to these parameters with high probability. Numerical simulations are performed using the proposed methods on a randomly generated system. The estimators for the QSR-dissipative parameters closely match the true values even when the signal-to-noise ratio is small, while the computed worst-case error bound is not violated in any simulation.