Distributed finite-time observer for LTI systems: A kernel-based approach

The problem of distributed state estimation of a linear-time-invariant (LTI) system is addressed in this paper. Given a directed communication network, the full state vector can be reconstructed at an appointed node under the assumption of an open Hamiltonian path. By a suitably designed coordinate transformation, the initial conditions of the subsystems can be estimated successively along the path. Thanks to the Volterra integral operator induced by non-asymptotic kernel functions, the estimation task at each agent can be achieved within a predefined finite time and transmitted to the next node. As such, the instant state vector can be reconstructed at the end node after a finite time interval. Such a scheme is prone to reduce the communication burden. Extensive numerical examples are conducted to verify the effectiveness of the proposed observer in both noise-free and noisy scenarios.