Design of developed distributed observers for nonlinear time-delay systems

This paper considers a distributed observer design for a class of nonlinear systems with time delays in a network. Specifically, each distributed observer has access to partial output as it communicates with its neighboring observers through consensus protocols defined on the network. The network includes N local observers where adjacent observers transmit and receive information through a delayed telecommunication graph network. The design method is based on Lipschitz condition of nonlinear terms while having time-delay cases in view. Appropriate selection of Lyapunov functions is made and the Jensen inequality applied in delayed nonlinear systems in undirected, strongly connected, and directed networks containing spanning trees. Also, via the design algorithm, the necessary and sufficient conditions for the design of parameters are defined so as to stabilize the error dynamics. Finally, numerical simulations are provided to verify the effectiveness of the proposed method.