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Simple Stabilization Design for Perturbed Time-Delay Systems

Chien-Hua Lee
Department of Electrical Engineering, Cheng-Shiu University, Kaohsiung City 83347, Taiwan

Abstract—In this paper, the stabilization design problem for the parametric perturbed systems with a time delay has been addressed. The perturbations are time-varying. Selecting a positive matrix Q and utilizing some linear algebraic techniques, we develop a simple upper solution bound of the Riccati equation and then applying it to the Riccati equation approach, a new condition for testing the stabilizability is proposed. Although the Riccati equation approach is adopted, the obtained stabilizability condition is independent of any Riccati equation and hence can be tested easily. It is shown that this condition is sharper than a previous one. Furthermore, the corresponding stabilization controllers are developed. These controllers are very simple and hence are easy to be implemented. A numerical algorithm is also presented to construct the controllers.
Index Terms—stabilization, time-delay, parametric perturbation, the Riccati equation approach; upper solution bound

Cite: Chien-Hua Lee, "Simple Stabilization Design for Perturbed Time-Delay Systems," International Journal of Electrical and Electronic Engineering & Telecommunications, Vol. 8, No. 3, pp. 158-162, May 2019. Doi: 10.18178/ijeetc.8.3.158-162