An Adaptive Distributed Observer for a Class of Discrete-Time Uncertain Linear Leader Systems Over Jointly Connected Switching Networks

This article proposes an output-based adaptive distributed observer for a class of discrete-time uncertain linear leader systems. The leader system is neutrally stable with unknown parameters in its system matrix. Such a leader system can produce discrete-time multitone sinusoidal signals with arbitrary magnitudes, arbitrary phases, and unknown frequencies. The adaptive distributed observer for the uncertain leader system is obtained via a two-step design. In the first step, both the state and the unknown parameters are estimated by the recent techniques for estimating the unknown frequencies of discrete-time multitone sinusoidal signals. In the second step, a state-based adaptive distributed observer over jointly connected switching networks for the estimated unknown parameters and the estimated state of the leader system is designed. It is shown that the proposed output-based adaptive distributed observer is capable of estimating the state of the leader system over jointly connected switching networks, as well as estimating the unknown parameters in the uncertain system matrix of the leader system. A numerical example is presented to show the effectiveness of our design.