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In this paper, we investigate the estimator-based output feedback controlproblem of multi-delay systems. This work is an extension of recently developedoperator-value LMI framework for infinite-dimensional time-delay systems. Basedon the optimal convex state feedback controller and generalized Luenbergerobserver synthesis conditions we already have, the estimator-based outputfeedback controller is designed to contain the estimates of both the presentstate and history of the state. An output feedback controller synthesiscondition is proposed using SOS method, which is expressed in a set of LMI/SDPconstraints. The simulation examples are displayed to demonstrate theeffectiveness and advantages of the proposed results.

Estimator-Based Output-Feedback Stabilization of Linear Multi-Delay Systems using SOS