State and unknown input simultaneous estimation for a class of nonlinear systems with time-delay

For a class of nonlinear systems with time-delay in state and unknown input signal, a simultaneous state and unknown input signal estimation technique is developed. The delays include three types. The systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. By constructing an appropriate augmented matrix, the nonlinear system is expressed into a generalized singular system. Upon satisfying some conditions, the observer design problem can be solved via the Riccati inequality or the linear matrix inequality-based technique. At the same time, the generalized inverse method is supplied. Sufficient conditions for asymptotic estimation convergence are established. The simulation includes three examples, and every example includes two schemes. One scheme ignores the influence of the time-delay. The other scheme deals with the influence of the time-delay using the proposed method. The simulation results show the efficiency of the proposed method.