Notions of observability for uncertain linear systems with structured uncertainty

This paper introduces a notion of observability for a class of uncertain linear systems with structured uncertainty. In the uncertain systems under consideration, the uncertainty is described by averaged integral quadratic constraints. In order to define a notion of observability for uncertain linear systems, the paper introduces a robust observability function which extends the usual definition of the observability Gramian to the case of uncertain systems. Using this observability function, a corresponding unobservable cone is defined, and an uncertain system is said to be robustly observable if this cone contains only the origin. The paper presents an algorithm for finding the robust observability function and corresponding unobservable cone. This algorithm involves solving a parameterized Riccati differential equation.