2010
DOI: 10.1155/2010/108218
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Abstract: Systems are considered related to the control of processes described by oscillating second-order systems of differential equations with a single delay. An explicit representation of solutions with the aid of special matrix functions called a delayed matrix sine and a delayed matrix cosine is used to develop the conditions of relative controllability and to construct a specific control function solving the relative controllability problem of transferring an initial function to a prescribed point in the phase sp… Show more

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Cited by 13 publications
(18 citation statements)
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“…So, differentiating this formula twice and applying (4) of Lemma 4 result in (11). Hence, one can see that function ( ) given by (70) really solves (11) and satisfies initial condition (8) and, moreover, that ∈ 2 ((0, ∞), R ).…”
Section: Resultsmentioning
confidence: 92%
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“…So, differentiating this formula twice and applying (4) of Lemma 4 result in (11). Hence, one can see that function ( ) given by (70) really solves (11) and satisfies initial condition (8) and, moreover, that ∈ 2 ((0, ∞), R ).…”
Section: Resultsmentioning
confidence: 92%
“…Motivated by delayed exponential representing a solution of a system of differential or difference equations with one or multiple fixed or variable delays [1][2][3][4][5][6], which has many applications in theory of controllability, asymptotic properties, boundary-value problems, and so forth [3][4][5][7][8][9][10][11][12][13][14][15], we extended representation of a solution of a system of differential equations of second order with delay [1] ( ) = − 2 ( − ) (1) to the case of two delays…”
Section: Introductionmentioning
confidence: 99%
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“…Further generalizations of (1.3) whose solutions involve the matrix sine and cosine have a right-hand side f (t, y(t)) + Bu(t), where u(t) is a control vector and B a matrix [34], possibly with a delayed linear term Ay(t − τ ) for a constant delay τ > 0 [9].…”
Section: A457mentioning
confidence: 99%
“…Thus, the notion of a functional differential equation was introduced by Myshkis [13] in 1949. A further progress have been made to study systems with delays in the past 50 years ( [14], [2] and the references therein); main ideas concerning the work in this area can be found in e.g. Krasovskii [8] (time-domain approach, extension of the Lyapunov second method to functional differential equations).…”
Section: Introductionmentioning
confidence: 99%