Robust Adaptive Memoryless Observer Design for MIMO Systems with Unknown Time-delays

This paper focuses on designing a state observer for MIMO systems with unknown nonlinearities and time-delays. Although numerous observers have been developed in recent decades, handling unknown nonlinearities and time-delays remains as an open problem. Under assumptions of bounded unknown delays, system observability, and satisfaction of norm-bounded and matching condition, a robust memoryless observer is developed, which integrates adaptive parameter estimation with σ-modification and robust compensation to address nonlinearities. Unlike observers that require precise delay or historical data, the proposed observer, without requiring explicit time-delay information, relies solely on current system information, making it suitable for practical application. Additionally, a novel robust compensation term and adaptive law different from the previous ones are developed, offering meaningful theoretical advancements. The convergence of the observer is rigorously proven using the Lyapunov methods. Numerical simulations under two different control inputs demonstrate the effectiveness of the proposed approach.