Valery Y. Glizer, $H_{\infty}$ control of singularly perturbed time delay systems: The separation of motions approach, Vol. 2026 (2026), No. 35, pp. 1-20

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DOI: 10.23952/cot.2026.35

Received March 30, 2025; Accepted July 24, 2025; Published online April 10, 2026

Abstract. An infinite horizon $H_{\infty}$ state-feedback control problem for singularly perturbed linear systems with multiple pointwise and distributed small state delays in the dynamics is considered. This problem is solved by the separation of motions method. Due to this method, the original $H_{\infty}$ control problem is decomposed asymptotically into two much simpler parameter-free $H_{\infty}$ control problems, the slow and fast ones. A solution (controller) of the original problem is obtained as a proper composition of solutions of the slow and fast problems. Gain matrices of this controller are parameter-free, and it solves the original problem for all sufficiently small values of the parameter of singular perturbation. An illustrative example is presented.

How to Cite this Article:
V. Y. Glizer, $H_{\infty}$ control of singularly perturbed time delay systems: The separation of motions approach, Commun. Optim. Theory 2026 (2026) 35.