Observer design for a class of Lipschitz nonlinear systems with delayed outputs: time-varying delay

In this paper a design of an observer for Lipschitz nonlinear systems in the presence of time-varying delay in outputs measurements is proposed. The structure of the proposed observer is based on the presence of a proportional integral term which permits the compensation of delay in the measurements outputs. The observer gain is a function of the maximum bound of the delay, the parameters of the system and it is calculated by the resolution of given LMI equation. The Lyapunov-Krasovskii functional is used to prove the asymptotical convergence to zero of the observation error. This observer can be applied to the case of systems with variable piecewise delay continuous functions, as for example, in the case of systems with piecewise delay constant functions of time and the case of time-discrete measurements with constant variable delay. The observer is validated into a Free Piston Stirling Engine model and the results were satisfactory, with a time-varying delay in piecewise randomly