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A New Observer Design for Systems in Presence of Time-varying Delayed Output Measurements

Boubekeur Targui, Omar Hernández-González*, Carlos-Manuel Astorga-Zaragoza, Gerardo-Vicente Guerrero-Ramírez, and María-Eusebia Guerrero-Sánchez
International Journal of Control, Automation, and Systems, vol. 17, no. 1, pp.117-125, 2019

Abstract : "This paper presents a state observer for linear systems and Lipschitz nonlinear systems with delayed output measurements, which are affected by a known and bounded time-varying delay. The structure of the proposed observer is based on a proportional-integral term, which allows to compensate the time-varying delay. The observer gain depends on the maximum bounded delay. This gain is computed by a Linear Matrix Inequality (LMI) approach. The observer exhibits good performance for state estimation of the system despite the presence of significantly long delay. A Lyapunov-Krasovskii functional is used to prove the asymptotical convergence to zero of the observation error. This observer is applied to the case of systems with time-varying delay whose dynamic is described by a piecewise differentiable function. Examples and numerical simulations are provided in order to support the validity of the main results."

Keyword : Lyapunov-Krasovskii and linear matrix inequality, time-varying delay

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