Design of a decentralized detection filter for a class of interconnected LTI systems

Abstract

In this thesis, we consider the problem of designing a decentralized detection filter for a class of homogeneous interconnected systems. In this class of systems, all subsystems have an identical structure. A fault in a subsystem propagates via interactions with other subsystems in the collection. We provide a computational algorithm for calculating the local detection filter gain matrix, L; this algorithm is computationally (marginally) better than other existing algorithms and involves formulating the detection spaces of faults in terms of unobservable subspaces of successively lower order systems. The decentralized detection filter is composed of interacting detection filters, one for each subsystem. We assume communication of state estimates amongst subsystems to be feasible. A concern, dealt with here, is that of propagation of state estimation errors. It is treated as [H] filtering problem with full state information, by requiring the transfer function from the propagated input of the [i]th subsystem to that of the (i+1)st subsystem to have a magnitude less than unity at all frequencies.