Observer based memoryless output feedback stabilization for linear systems with both complex input and output time delays

This paper addresses the stabilization problem for linear systems with both complex input and output delays, considering in both continuous-time and discrete-time domains. The proposed methodology begins by applying the Artstein transformation to reduce the system order, resulting in a delay-free system that is equivalent to the original system. A unified functional observer is then designed, which includes both full-order and reduced-order observers as special cases. Next, a controller is developed based on the functional observer and truncated pseudo-predictor feedback, utilizing the unique positive definite solution to the parametric Lyapunov equation (PLE). By leveraging the properties of the PLE, the infinite-dimensional terms in the controller are justifiably neglected, leading to a finite-dimensional controller. The asymptotic stability of the resulting closed-loop system is rigorously proven using the Lyapunov-Krasovskii functional approach. Finally, the effectiveness of the proposed methods is demonstrated through a spacecraft rendezvous model and a numerical example.