Adaptive distributed unknown input observers for interconnected linear descriptor systems

We propose an adaptive distributed algorithm for distributed observers of linear time-invariant descriptor systems. In the proposed algorithm, the interconnection gains of the resulting distributed unknown input observers are adjusted adaptively and the adaptation law is obtained by a Lyapunov-redesign approach. The scheme uses adaptive gains for each pairwise difference in the coupling term, which are adjusted in proportion to the pairwise differences of the state estimates. A special case where a single adaptive gain is used in each node to uniformly penalise all pairwise differences of the state estimates in the coupling term is also presented. Stability of the proposed schemes is proved and it is shown to be independent of the graph topology of the network. A numerical example is provided to illustrate the performance of the proposed adaptive distributed unknown input observers algorithm and to compare it with the non-interacting (local) unknown input observers.