  This paper presents a sound and complete fault detection approach for
cyber-physical systems represented by hidden-mode switched affine models with
time varying parametric uncertainty. The fault detection approach builds upon
techniques from model invalidation. In particular, a set-membership approach is
taken where the noisy input-output data is compared to the set of behaviors of
a nominal model. As we show, this set-membership check can be reduced to the
feasibility of a mixed-integer linear programming (MILP) problem, which can be
solved efficiently by leveraging the state-of-the-art MILP solvers. In the
second part of the paper, given a system model and a fault model, the concept
of T-detectability is introduced. If a pair of system and fault models
satisfies T-detectability property for a finite T, this allows the model
invalidation algorithm to be implemented in a receding horizon manner, without
compromising detection guarantees. In addition, the concept of
weak-detectability is introduced which extends the proposed approach to a more
expressive class of fault models that capture language constraints on the mode
sequences. Finally, the efficiency of the approach is illustrated with
numerical examples motivated by smart building radiant systems.
