Kobayashi, Toshihiro Input-output representations of spectral systems and adaptive controls. (English) Zbl 0647.93009 Int. J. Syst. Sci. 19, No. 5, 713-732 (1988). Static input-output representations and dynamical input-output representations are presented for the class of distributed parameter systems generated by spectral operators. These representations have forms independent of the dimensions of the system. Thus they are very useful in designing an adaptive control system for an infinite-dimensional system. Reviewer: M.Megan Cited in 1 Document MSC: 93B15 Realizations from input-output data 93C25 Control/observation systems in abstract spaces 93C40 Adaptive control/observation systems 47B40 Spectral operators, decomposable operators, well-bounded operators, etc. 93C20 Control/observation systems governed by partial differential equations 93D15 Stabilization of systems by feedback Keywords:input-output representations; distributed parameter systems; spectral operators; adaptive control; infinite-dimensional system PDFBibTeX XMLCite \textit{T. Kobayashi}, Int. J. Syst. Sci. 19, No. 5, 713--732 (1988; Zbl 0647.93009) Full Text: DOI References: [1] DOI: 10.1080/00207178408933195 · Zbl 0541.93041 · doi:10.1080/00207178408933195 [2] DOI: 10.1007/BFb0006761 · doi:10.1007/BFb0006761 [3] DOI: 10.1007/BFb0005037 · doi:10.1007/BFb0005037 [4] KATO T., Perturbation Theory for Linear Operators (1966) · Zbl 0148.12601 [5] DOI: 10.1016/0167-6911(83)90035-X · Zbl 0512.93031 · doi:10.1016/0167-6911(83)90035-X [6] KWAKERNAAK H., Linear Optimal Control Systems (1972) · Zbl 0276.93001 [7] LANDAU Y. D., Adaptive Control (1979) [8] LASALLE , J. P. , and RATH , R. J. , 1963 , Eventual stability .Proc. 2nd IF AC CongressPt 1 , Basle , pp. 550 – 560 . [9] DOI: 10.1016/0022-247X(78)90229-9 · Zbl 0371.93010 · doi:10.1016/0022-247X(78)90229-9 [10] DOI: 10.1109/TAC.1975.1101095 · Zbl 0319.93039 · doi:10.1109/TAC.1975.1101095 [11] DOI: 10.1137/0321050 · Zbl 0524.93054 · doi:10.1137/0321050 [12] SCHWARTZ J. T., Pacific J. Math. 4 pp 415– (1954) [13] DOI: 10.1137/0319048 · Zbl 0482.93035 · doi:10.1137/0319048 [14] WERMER P., Pacific J. Math. 4 pp 355– (1954) · Zbl 0056.34701 · doi:10.2140/pjm.1954.4.355 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.