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Persistent bounded disturbance rejection for uncertain time-delay systems. (English) Zbl 1301.93144
Summary: This paper considers the problem of persistent bounded disturbance rejection for a class of time-delay systems with parametric uncertainty by Lyapunov function and positively invariant set analysis method. Sufficient conditions for internal stability and $$L_1$$-performance analysis are given in terms of linear matrix inequalities (LMIs). Based on the results, a simple approach to the design of a linear state-feedback controller is presented to stabilize robustly the uncertain time-delay systems and achieve a desired level of disturbance attenuation. All the obtained conditions are delay-dependent. A numerical example is included to illustrate the proposed method.
##### MSC:
 93D21 Adaptive or robust stabilization 93B35 Sensitivity (robustness) 93C73 Perturbations in control/observation systems 93B52 Feedback control 93C41 Control/observation systems with incomplete information