Split-Spectrum Based Distributed Estimator for a Continuous-Time Linear System on a Time-Varying Graph

A simply structured distributed estimator is described for estimating the state of a continuous-time, jointly observable, input free, multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose neighbor graphs switch according to a switching signal with a dwell time, or switch arbitrarily under appropriate assumptions. The estimator is guaranteed to solve the problem, provided a network-widely shared gain is sufficiently large. The lower bound of the gain is derived. This is accomplished by appealing to the 'split-spectrum' approach and exploiting several well-known properties of invariant subspace. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable.