Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

Vasilii Zaitsev and Inna Kim
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Vasilii Zaitsev: Laboratory of Mathematical Control Theory, Udmurt State University, 426034 Izhevsk, Russia
Inna Kim: Laboratory of Mathematical Control Theory, Udmurt State University, 426034 Izhevsk, Russia

Mathematics, 2021, vol. 9, issue 17, 1-16

Abstract: We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and its derivatives, and the output is a multidimensional vector of linear combinations of the state and its derivatives. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function by linear static output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for the solvability of the arbitrary coefficient assignment problem by the static output feedback controller. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We provide an example illustrating our results.

Keywords: linear differential equation; time-delay system; lumped delay; distributed delay; characteristic function coefficient assignment; stabilization; linear static output feedback (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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