Olbrot, A. W.; Pandolfi, L. Null controllability of a class of functional differential systems. (English) Zbl 0662.93008 Int. J. Control 47, No. 1, 193-208 (1988). The authors prove that spectral controllability implies null controllability for a class of functional differential equations. This assertion appears, as the authors mention, in earlier papers by Marchenko and by the reviewer who used results due to Watanabe. However this important paper presents the first clear and reliable proof, using algebraic methods. They show that null controllability is equivalent to the solvability of a certain matrix Bézout equation over appropriate subrings of the ring of entire functions. Then spectral controllability implies that this equation can be solved. Reviewer: F.Colonius Cited in 1 ReviewCited in 9 Documents MSC: 93B05 Controllability 34K35 Control problems for functional-differential equations 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 93B03 Attainable sets, reachability 93B25 Algebraic methods Keywords:spectral controllability; null controllability; functional differential equations; matrix Bézout equation PDFBibTeX XMLCite \textit{A. W. Olbrot} and \textit{L. Pandolfi}, Int. J. Control 47, No. 1, 193--208 (1988; Zbl 0662.93008) Full Text: DOI References: [1] BELLMAN R., Differential-difference Equations (1963) · Zbl 0105.06402 [2] BHAT K. P. M., I.E.E.E. Trans. autom. Control 21 pp 232– (1976) [3] BULATOV V. M., Diff. Urav. 10 pp 1946– (1974) [4] DOI: 10.1016/S0167-6911(84)80105-X · Zbl 0548.93010 · doi:10.1016/S0167-6911(84)80105-X [5] DOI: 10.1080/00207178608933506 · Zbl 0599.93047 · doi:10.1080/00207178608933506 [6] KUČERA V., Discrete Linear Controls: a Polynomial Equation Approach (1979) [7] DOI: 10.1080/00207728208926335 · Zbl 0478.93015 · doi:10.1080/00207728208926335 [8] DOI: 10.1109/TAC.1979.1102124 · Zbl 0425.93029 · doi:10.1109/TAC.1979.1102124 [9] MARCHENKO V., Probl. Control Inf. Theory 8 pp 422– (1979) [10] DOI: 10.1016/0005-1098(76)90013-3 · Zbl 0345.93023 · doi:10.1016/0005-1098(76)90013-3 [11] DOI: 10.1109/TAC.1978.1101879 · Zbl 0399.93008 · doi:10.1109/TAC.1978.1101879 [12] OLBROT A. W., Found. Control Engng 5 pp 79– (1980) [13] PANDOLFI L., Boll. Un. mat. ital., (IV) 11 pp 626– (1975) [14] SALAMON D., Control and Observation of Linear Neutral Functional Differential Equations (1985) [15] DOI: 10.1080/00207178408933183 · Zbl 0545.93011 · doi:10.1080/00207178408933183 [16] DOI: 10.1080/00207178308933098 · Zbl 0542.93061 · doi:10.1080/00207178308933098 [17] DOI: 10.1080/00207178308933119 · Zbl 0528.93037 · doi:10.1080/00207178308933119 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.