Design of a decentralized detection of interacting LTI systems

In this paper, the problem of designing a decentralized detection filter for a large homogeneous collection of LTI systems is considered. The collection of systems considered here draws inspiration from platoons of vehicles, and the considered interactions amongst systems in the collection are banded and lower triangular, mimicking the typical “look‐ahead” nature of interactions in a platoon of vehicles. A fault in a system propagates to other systems in the collection via such interactions. The decentralized detection filter for the collection is composed of interacting detection filters, one for each system. The feasibility of communicating the state estimates to other systems in the collection is assumed here. An important concern is the propagation of state estimation errors. In order that the state estimation errors not amplify as they propagate, a ℋ ∞ constraint on the state estimation error propagation dynamics is imposed. A sufficient condition for constructing a decentralized detection filter for the collection is presented. An example is provided to illustrate the design procedure.