Observer design for nonlinear systems with delayed output measurement

This paper deals with nonlinear observer design for systems with a long delay in the nonlinear outputs. The main idea behind this work consists of using a dynamic extension technique to transform a system with delayed nonlinear outputs into a system with linear outputs and a delay-dependent integral term in the dynamic process. First, a general result for arbitrary nonlinear structures is proposed, and then further contributions are provided for the specific family of systems in companion form. For systems in companion form, we obtain novel high-gain observer synthesis conditions. To relax the necessary conditions related to the observer design procedure, a different state observer structure is proposed, and analytical comparisons are provided. Moreover, to relax the design conditions, we propose an alternative design approach using a specific Lyapunov–Krasovskii functional, which allows accommodating long delays in the outputs.