Distributed state estimation for discrete-time uncertain linear systems over jointly connected switching networks

This paper proposes a constructive distributed adaptive observer design approach for jointly observable discrete-time uncertain linear time-invariant (LTI) systems over time-varying communication networks. In comparison with existing works, the approach developed in this work can guarantee distributed state estimation in the presence of sparse sensor arrangement, modeling uncertainties, and unreliable network communication. A discrete-time linear system decomposition method is first developed to mitigate the impact of the unknown parameters. A fully distributed discrete-time adaptive nonlinear observer is then designed for the decomposed system. The observer is composed of two time-varying discrete-time dynamics and two nonlinear mappings that establish the connection between the observed system's state and parameters and the states of the two time-varying dynamics. By establishing a discrete-time parametric representation of the measurement output, the parameter estimation problem is converted to a parameter identification problem, which is solved by the gradient-descent adaptive law in the proposed observer dynamics. The analysis shows that the estimation error system is asymptotically stable. Thus, the distributed discrete-time adaptive observer holds under the jointly observable condition in spite of system uncertainties and jointly connected communication networks. The robustness properties of the proposed distributed discrete-time adaptive observer in the presence of measurement noise are established using an input-to-state stability analysis.