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O.","family":"Anderson","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,5,24]]},"reference":[{"key":"2_CR1","unstructured":"C. A. Desoer and E. S. Kuh, Basic Circuit Theory, McGraw-Hill, 1970. (This text is valuable for various linear systems viewpoints, all within the framework of networks. The sorts of network descriptions used include ordinary differential equations like (1), state-variable systems like (2), impulse response description (related to (4)) and Laplace transform and Fourier transform descriptions. The latter two, though differing but trivially from the mathematical viewpoint in many cases, provide to an engineer vastly differing heuristically derived information.)"},{"key":"2_CR2","unstructured":"R. W. Brockett, Finite-Dimensional Linear Systems, John Wiley, 1970."},{"key":"2_CR3","unstructured":"R. E. Kalman, P. L. Falb and M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, 1969."},{"key":"2_CR4","unstructured":"B. D. O. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis; A Modern Systems Theory Approach, Prentice Hall, 1973. (This text discusses network theory almost exclusively using state-variable ideas. It contains a one chapter survey of many results concerning finite-dimensional linear systems)."},{"key":"2_CR5","unstructured":"B. D. O. Anderson and J. B. Moore, Linear Optimal Control, Prentice-Hall, 1971. (This book contains a discussion of observers, both in a deterministic framework and a stochastic framework \u2014the latter because one needs to model and cope with the effects of measurement noise picked up by the sensors associated with a physical linear system.)"},{"key":"2_CR6","unstructured":"L. A. Zadeh and C. A. Desoer, Linear System Theory-A State Space Approach, McGraw-Hill, 1963. (This book was the first to present system theory in a form that engineers could understand. It is a source of many valuable ideas.)"},{"key":"2_CR7","unstructured":"R. R. Mohler and A. Ruberti, eds., Theory and Application of Variable Structure Systems, Academic Press, 1972. (This book is a collection of papers, some offering examples of nonlinear systems)."},{"key":"2_CR8","doi-asserted-by":"crossref","unstructured":"D. G. Tucker, Circuits with Periodically-varying Parameters, Unending Modulators and Parametric Amplifiers, Van Nostrand, 1964.","DOI":"10.1049\/ree.1963.0035"},{"key":"2_CR9","unstructured":"M. Athans and P. L. Falb, Optimal Control, McGraw-Hill, 1966. (This book has a fairly lengthy introduction to linear systems theory before entering on a discussion of optimal control theory)."},{"key":"2_CR10","unstructured":"S. Ramo, J. R. Whinnery and T. van Duzen, Fields and Waves in Communication Electronics, Wiley, 1965."},{"key":"2_CR11","unstructured":"F. R. Gantmakher, Theory of Matrices, 2 vols., Chelsea, 1960."},{"key":"2_CR12","unstructured":"R. E. Bellman, Introduction to Matrix Analysis, McGraw-Hill, 1960."},{"key":"2_CR13","unstructured":"S. Barnett, Matrices in Control Theory, Van Nostrand, 1971."},{"key":"2_CR14","doi-asserted-by":"crossref","unstructured":"M. A. Arbib and E. G. Manes, Foundations of system theory: decomposable machines, Automatica, to appear. (This is an interesting paper, providing a better unification of some results of linear systems and group machines then hitherto available. Whether the approach will catch on with the control fraternity or not may well depend on what the contents of sequel papers are).","DOI":"10.1016\/0005-1098(74)90039-9"},{"key":"2_CR15","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1109\/TIT.1969.1054260","volume":"IT-15","author":"J. L. Massey","year":"1969","unstructured":"J. L. Massey, Shift-register synthesis and BCH decoding, IEEE Trans. Inf. Th. IT-15, 1969, 122\u2013127.","journal-title":"IEEE Trans. Inf. Th."},{"key":"2_CR16","doi-asserted-by":"publisher","first-page":"3404","DOI":"10.1073\/pnas.69.11.3404","volume":"69","author":"Y. Rouchaleau","year":"1972","unstructured":"Y. Rouchaleau, B. F. Wyman and R. E. Kalman, Algebraic structure of linear dynamical systems, III: realization theory over a commutative ring, Proc. Nat. Acad. Sci. 69, 1972, 3404\u20133406.","journal-title":"Proc. Nat. Acad. Sci."},{"key":"2_CR17","unstructured":"R. W. Brockett and J. L. Willems, Systems defined on modules and applications to the control of linear partial differential equations, Automatica, to appear."},{"key":"2_CR18","unstructured":"R. deB. Johnson, Linear systems over various rings, Report ESL-R-497, MIT, 1973."},{"key":"2_CR19","unstructured":"B. F. Wyman, Linear systems over rings of operators, this volume."},{"key":"2_CR20","first-page":"483","volume":"AC-17","author":"R. W. Brockett","year":"1973","unstructured":"R. W. Brockett and A. S. Willsky, Finite state homomorphic sequential machines, IEEE Trans. Auto. Cont. AC-17, 1973, 483\u2013490.","journal-title":"IEEE Trans. Auto. Cont."},{"key":"2_CR21","unstructured":"B. D. O. Anderson, M. A. Arbib and E. G. Manes, Finitary and infinitary properties in categorical realization theory, to appear."},{"key":"2_CR22","unstructured":"L. Schwartz, Th\u00e9orie des Distributions, 2 vols., Hermann, 1950,51."},{"key":"2_CR23","unstructured":"R. W. Newcomb, Linear Multiport Synthesis, McGraw-Hill, 1965."},{"key":"2_CR24","doi-asserted-by":"crossref","unstructured":"R. E. Kalman and M. L. J. Hautus, Realization of continuous-time linear dynamical systems: rigorous theory in the style of Schwartz, Proc. NRL Conf. on Differential Equations, 1971.","DOI":"10.1016\/B978-0-12-743650-0.50018-6"},{"key":"2_CR25","unstructured":"E. W. Kamen, On an algebraic representation of continuous-time systems"},{"key":"2_CR26","doi-asserted-by":"crossref","unstructured":"M. R. Wohlers, Lumped and Distributed Passive Networks, Academic Press, 1969. (See also issues of the IEEE Transactions on Circuit Theory for material on lumped-distributed systems).","DOI":"10.1016\/B978-1-4831-9621-3.50006-0"},{"key":"2_CR27","unstructured":"E. W. Kamen, Control of linear continuous-time systems defined over rings of distributions, this volume."}],"container-title":["Lecture Notes in Computer Science","Category Theory Applied to Computation and Control"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-07142-3_60.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T19:56:50Z","timestamp":1605643010000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-07142-3_60"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1975]]},"ISBN":["9783540071426","9783540374268"],"references-count":27,"URL":"http:\/\/dx.doi.org\/10.1007\/3-540-07142-3_60","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"published":{"date-parts":[[1975]]}}}