Controllability, Observability and Stability of Linear Systems

Previous article Next article Controllability, Observability and Stability of Linear SystemsL. M. Silverman and B. D. O. AndersonL. M. Silverman and B. D. O. Andersonhttps://doi.org/10.1137/0306010PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 L. A. Zadeh and , C. A. Desoer, Linear System Theory, McGraw-Hill, New York, 1963 Google Scholar2 Nam P. Bhatia, On exponential stability of linear differential systems, J. Soc. Indust. Appl. Math. Ser. A Control, 2 (1964), 181–191 MR0182774 0151.11902 LinkGoogle Scholar3 R. E. Kalman, Mathematical description of linear dynamical systems, J. SIAM Control Ser. A, 1 (1963), 152–192 (1963) MR0152167 0145.34301 Google Scholar4 R. E. Kalman and , J. E. Bertram, Control system analysis and design via the “second method” of Lyapunov. I. Continuous-time systems, Trans. ASME Ser. D. J. Basic Engrg., 82 (1960), 371–393 MR0157810 CrossrefGoogle Scholar5 D. C. Youla, On the stability of linear systems, IEEE Trans. Circuit Theory, CT-10 (1963), 276–279 CrossrefGoogle Scholar6 C. A. Desoer and , A. J. Thomasian, A note on zero-state stability of linear systems, Proc. 1st Allerton Conference on Circuit and System Theory, University of Illinois, Urbana, 1963, 50–52 Google Scholar7 R. E. Kalman, On the stability of time-varying linear systems, IRE Trans. Circuit Theory, CT-9 (1962), 420–422 CrossrefGoogle Scholar8 R. E. Kalman, Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana (2), 5 (1960), 102–119 MR0127472 0112.06303 Google Scholar9 Oskar Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z., 32 (1930), 703–728 10.1007/BF01194662 MR1545194 CrossrefGoogle Scholar10 R. W. Brockett, The status of stability theory for deterministic systems, IEEE Internat. Automatic Control, AC-11 (1966), 596–606 10.1109/TAC.1966.1098354 CrossrefISIGoogle Scholar11 R. W. Brockett, Poles, zeros and feedback; state space interpretation, IEEE Trans. automatic control, AC-10 (1965), 129–134 10.1109/TAC.1965.1098118 CrossrefISIGoogle Scholar12 R. W. Brockett and , H. B. Lee, Frequency-domain instability criteria for time-varying and nonlinear systems, Proc. IEEE, 55 (1967), 604–618 CrossrefISIGoogle Scholar13 L. M. Silverman and , H. E. Meadows, Controllability and observability in time-variable linear systems, SIAM J. Control, 5 (1967), 64–73 10.1137/0305005 MR0209043 0163.11001 LinkGoogle Scholar14 Leonard H. Haines and , Leonard M. Silverman, Internal and external stability of linear systems, J. Math. Anal. Appl., 21 (1968), 277–286 10.1016/0022-247X(68)90213-8 MR0223669 0155.12903 CrossrefISIGoogle Scholar15 B. D. O. Anderson, Stability properties of linear systems in phase-variable form, Proc. Inst. Elec. Engrs., 115 (1968), 340–341 MR0305878 CrossrefISIGoogle Scholar16 L. M. Silverman, Transformation of time-variable systems to canonical (phase-variable) form, IEEE Trans. Automatic Control, AC-11 (1966), 300–303 10.1109/TAC.1966.1098312 CrossrefISIGoogle Scholar17 Wilfred Kaplan, Operational methods for linear systems, Addison-Wesley Series in Mathematics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1962xi+577 MR0139903 0143.11204 Google Scholar18 L. M. Silverman, Stable realization of impulse response matrices, IEEE International Convention Record, 15 (1967), 32–36 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Harmonic Framework for Controllability in Linear Continuous‐Time Periodic Systems7 May 2007 | SIAM Journal on Control and Optimization, Vol. 46, No. 2AbstractPDF (266 KB)Internal and External Stability of Linear Time-Varying Systems17 February 2012 | SIAM Journal on Control and Optimization, Vol. 20, No. 3AbstractPDF (576 KB)On the Input-Output Stability of Linear Time-Varying Systems12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 38, No. 1AbstractPDF (1201 KB)A Multi-Time Scale Method in Almost-Periodic Stability Problems17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 9, No. 6AbstractPDF (1630 KB)Estimation and Feedback in Linear Time-Varying Systems: A Deterministic Theory18 July 2006 | SIAM Journal on Control, Vol. 13, No. 2AbstractPDF (1971 KB)State in Hilbert Space2 August 2006 | SIAM Review, Vol. 15, No. 2AbstractPDF (2221 KB)Stabilization of Linear Systems18 July 2006 | SIAM Journal on Control, Vol. 10, No. 4AbstractPDF (1124 KB)Some Sufficient Conditions for the Global and Local Controllability of Nonlinear Time-Varying Systems18 July 2006 | SIAM Journal on Control, Vol. 8, No. 4AbstractPDF (725 KB)New Results in Linear System Stability18 July 2006 | SIAM Journal on Control, Vol. 7, No. 3AbstractPDF (1356 KB)Equivalent Realizations of Linear Systems12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 17, No. 2AbstractPDF (1627 KB) Volume 6, Issue 1| 1968SIAM Journal on Control History Submitted:18 May 1967Published online:18 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0306010Article page range:pp. 121-130ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics