Nonlinear observer design for discrete MIMO systems with unknown time delay

This paper proposes an adaptive observer for discrete MIMO systems with unknown dynamics and time-delay. The case that the system output equation has time-delay and nonlinearities is also studied. The delayed states in the system are with a nonlinear form and only the estimated delay is utilized. By using a high-order neural network (HONN), the precise system model, and the Lipschitz or norm-boundedness assumption of unknown nonlinearities are not required. A novel converse Lyapunov lemma is also developed to prove the uniform ultimate boundedness (UUB) of the proposed observer. Applicability of the presented scheme is verified by simulation.