Polynomial-Time Probabilistic Observability Analysis of Sampled-Data Piecewise Affine Systems

This paper proposes a polynomial-time probabilistic approach to solve the observability problem of sampled-data piecewise affine systems. First, an algebraic characterization for the system to be observable is derived. Next, based on the characterization, we propose a randomized algorithm that can determine with a probabilistic accuracy if the system is observable or not. Finally, it is shown with some examples, for which it is hopeless to check the observability in a deterministic way, that the proposed algorithm is very useful.