On detectability of stochastic systems

We discuss notions of detectability for stochastic linear control systems of Itˆo type. A natural concept of detectability requires a non-zero output, if the state process is unstable. We show that this property can equivalently be characterized by a generalized version of the Hautus-test. The proof is based on spectral theory for positive operators. Key words: Detectability, Observability, Stochastic systems, Positive operators, Lyapunov equation

• Type: Journal
• Year: 2007
• Where: AUTOMATICA
• Authors: Tobias Damm
• Keywords: AUTOMATICA 2007, Detectability, Positive Operators, Stochastic Linear Control