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Home » Issues » Archive of Issues » 2023 - 2 issue » pp. 329-347

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Belarus Grodno
Year
2023
Volume
33
Issue
2
Pages
329-347
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Section Mathematics
Title Estimation of the solution of asymptotically observable linear completely regular differential-algebraic systems with delay
Author(-s) Khartovskii V.E.a
Affiliations Grodno State Universitya
Abstract In the article, a problem of solution estimation for linear autonomous completely regular differential-algebraic systems with many commensurate delays is investigated. The class of completely regular differential-algebraic systems with delay under study includes the classes of linear systems of delayed and neutral types; in addition, the analysis of continuous-discrete systems is reduced to completely regular systems. For linear autonomous completely regular differential-algebraic systems with many commensurate delays, the property of asymptotic observability is determined, which are characterized by the fact that all solutions generating the same output signal are indistinguishable in the future. Conditions for asymptotic observability expressed in terms of the parameters of the original system are formulated and proved. For asymptotically observable systems, a solution estimation procedure is proposed, the implementation of which consists of the following steps. First, using the observed output, a linear autonomous non-homogeneous asymptotically observable retarded type system with a non-homogeneous part depending on the output is put in correspondence with the original system. The solution of the new system uniquely determines the solution of the original system. Then a transformation is constructed that reduces the matrices of the retarded type system to a certain form. After that, with the help of a finite chain of observers, the solution is evaluated. The results of the presented study are applicable to systems that do not have the property of final observability, which makes it possible to significantly reduce the requirements for observing organs when modeling the corresponding objects of the real world.
Keywords linear autonomous completely regular differential-algebraic system, delay, observed output signal, solution estimate, asymptotic observer
UDC 517.977
MSC 93C41, 34K34, 34K35
DOI 10.35634/vm230210
Received 21 February 2023
Language Russian
Citation Khartovskii V.E. Estimation of the solution of asymptotically observable linear completely regular differential-algebraic systems with delay, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 2, pp. 329-347.
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