This paper investigates the simultaneous design of a controller and Luenberger state observer for systems with time-delays, external disturbances, uncertainties, modeling errors, and unknown nonlinear perturbations. The state-feedback control approach and state-observer existence conditions are formulated using the Linear Matrix Inequalities (LMIs). By defining the estimation error, the equations of the closed-loop system are rewritten. External disturbances, uncertainties, unknown nonlinear perturbations, and constant time-delays are considered in system modeling. By using LMI techniques, the estimation error is converged to zero. Therefore, the time-delays, uncertainties, and external disturbance effects on the system output, which have not been considered simultaneously before, are minimized, and the closed-loop system is stabilized. The performance of the proposed approach is verified by simulation of two examples, Flexible-Link Manipulator (FLM) dynamics, and Continuous Stirred Tank Reactor (CSTR) system. These examples illustrate the reliability of the suggested method.
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Karami et al. (2023) studied this question.