Completely Distributed Observer Design of LTI Systems with Disturbances

In this paper, the distributed state estimation problem of a linear time invariant system with external disturbance by using multiple measurements is studied, where each sensor of the measurement only has to measure a part of outputs. The investigations are carried out by designing a novel estimation algorithm under the jointly observable assumption of the measured outputs, where both the high-gain observer technique and the matrix coupling based adaptive consensus protocol are used. It is proved that the error between the state and the estimation can be made arbitrarily small by tuning the high-gain parameter in the high-gain observer and the adaptive parameter in the adaptive consensus protocol. Simulations are provided to support the theoretical results.