Developing a Design of Distributed Sliding mode Observers for Nonlinear Systems with Time – Delay and Applying uncertainty

This paper propounds a distributed observer design for a class of nonlinear systems with time delays and applying uncertainty in an undirected network. In particular, each distributed observer has availability, to partial output as it communicates with its neighboring observers through consensus protocols defined on the undirected network. The network includes M local observers where adjacent observers transmit and receive data through a delayed telecommunication graph network with uncertainty. The design method is based on Lipschitz condition of nonlinear terms. Appropriate selection of Lyapunov functions is created, and the Jensen inequality applied in undirected network. Also, by 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 contrast the effectiveness of the proposed method.