Set Descripitions of White Noise and Worst Case Induced Norms Connections to the Behavioral Framework

Fernando Paganini, EE, Caltech

In this talk we provide a framework for analyzing white noise disturbances in linear systems. Rather than the usual stochastic approach, noise signals are described as elements in sets and the disturbance rejection properties of the system are described in a worst case setting.The description is based on properties of finite records of signals, which may be verified directly on experimental data. Bounds of system gain for input signals in these sets are given, and their asymptotic behavior for long data records is analyzed. It is further shown that set characterizations of "whiteness" of signals can be recast as uncertain behavioral equations. This allows us to pose the "robust H2" analysis question as an robust stability analysis problem in the behavioral framework.