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Belarus Grodno; Minsk
Section  Mathematics 
Title  Calming the solution of systems of neutral type with many delays using feedback 
Author(s)  Metel'skii A.V.^{a}, Khartovskii V.E.^{b}, Urban O.I.^{b} 
Affiliations  Belarusian National Technical University^{a}, Grodno State University^{b} 
Abstract  This paper examines the following problem: a linear autonomous differentialdifference system of neutral type with delay in state requires ensuring its complete calming by feedback. To solve this problem linear autonomous dynamic differentialdifference controller with state feedback is proposed; this controller does not exclude a closed system from the original class of linear autonomous systems of neutral type. Sufficient condition for the existence of such a controller coincides with the criterion of complete controllability. In addition, the closed system has a finite spectrum, which simplifies greatly the problem of calculating the current state during the technical implementation of the controller. The basic idea of research is to select parameters for the controller so that the closed system becomes pointdegenerated in directions corresponding to phase components of the original (open) system. To do this, the original system is first converted via feedback to the singleinput system of retarded type. Further, for the resulting object the dynamic controller that provides the degeneracy of the corresponding phase components is constructed. The proposed procedure for constructing the control action is based on the algebraic properties of shift operator and does not involve calculating the roots of characteristic quasipolynomial of the original system. It can be used to provide full calming as well as exponential stability to a closed system. However, in the latter case it is necessary to use dynamic controller with state feedback of integral type. 
Keywords  differencedifferential system, neutral type, complete controllability, controller, feedback, point degeneration 
UDC  517.977 
MSC  93B05, 93С15 
DOI  10.20537/vm140304 
Received  30 June 2014 
Language  Russian 
Citation  Metel'skii A.V., Khartovskii V.E., Urban O.I. Calming the solution of systems of neutral type with many delays using feedback, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 3, pp. 4051. 
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