Abstract
Feedback control of linear neutral (and retarded) time-delay systems with one or more non-commensurate time delays is studied. A new (algebraic) notion of stability, called pointwise stability, is defined and is shown to be generically equivalent to uniform asymptotic stability independent of delay. Necessary and sufficient conditions are then given for regulability, that is, for the existence of a dynamic output feedback compensator with pure delays such that the closed-loop system is internally pointwise stable (and thus stable independent of delay). Necessary and sufficient conditions involving matrix-fraction descriptions are also given for the existence of a state realization which is regulable. Finally, the problem of stabilization using nondynamic state feedback is briefly considered in the case when the system's input matrix has constant rank.
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This work was supported in part by the U.S. Army Research Office under Contract No. DAAG29-81K-0166 and in part by the National Science Foundation under Grant No. ECS-8200607.
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Kamen, E.W., Khargonekar, P.P. & Tannenbaum, A. Pointwise stability and feedback control of linear systems with noncommensurate time delays. Acta Appl Math 2, 159–184 (1984). https://doi.org/10.1007/BF00046577
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DOI: https://doi.org/10.1007/BF00046577