Observer design for lipschitz nonlinear systems with time-varying output and state delays

This research paper deals with a novel delay-range-dependent approach for observer design for systems with time-varying delay in the state variables and the output measurement vector. Lyapunov Karasovskii (LK) functional, Jensen´s inequality and linear matrix inequality(LMI) tools are employed to derive the stability conditions ensuring the state estimation error to asymptotically converge to the origin. Further, as particular cases of proposed design methodology, delay-range-dependent design conditions are separately deduced for systems with state delays or output delays. Numerical example is simulated to validate the efficiency of the derived results.