Matrix Equation $XA + BX = C$
1968; Society for Industrial and Applied Mathematics; Volume: 16; Issue: 1 Linguagem: Inglês
10.1137/0116017
ISSN1095-712X
Autores Tópico(s)Matrix Theory and Algorithms
ResumoPrevious article Next article Matrix Equation $XA + BX = C$R. A. SmithR. A. Smithhttps://doi.org/10.1137/0116017PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. Barnett and , C. Storey, Some applications of the Lyapunov matrix equation, J. Inst. Math. Appl., to appear Google Scholar[2] Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960xx+328 MR0122820 0124.01001 Google Scholar[3] W. G. Bickley and , J. McNamee, Matrix and other direct methods for the solution of systems of linear difference equations, Philos. Trans. Rov. Soc. London Ser. A, 252 (1960), 69–131 MR0114067 0092.13001 CrossrefISIGoogle Scholar[4] Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964xi+257 MR0175290 0161.12101 Google Scholar[5] Er-chieh Ma, A finite series solution of the matrix equation $AX-XB=C$, SIAM J. Appl. Math., 14 (1966), 490–495 10.1137/0114043 MR0201456 0144.27003 LinkISIGoogle Scholar[6] D. E. Rutherford, On the solution of the matrix equation $AX+XB=C$, Nederl. Akad. Wetensch. Proc. Ser. A, 35 (1932), 53–59 0004.19502 Google Scholar[7] R. A. Smith, Bounds for quadratic Lyapunov functions, J. Math. Anal. Appl., 12 (1965), 425–435 10.1016/0022-247X(65)90010-7 MR0190475 0135.29802 CrossrefISIGoogle Scholar[8] R. A. Smith, Matrix calculations for Liapunov quadratic forms, J. Differential Equations, 2 (1966), 208–217 10.1016/0022-0396(66)90044-1 MR0188557 0151.02206 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Iterative Approach for Reduction of Index-2 Periodic Models Using Generalized Inverse ProcedureProceedings of Seventh International Congress on Information and Communication Technology | 3 August 2022 Cross Ref Combined real and imaginary parts method for solving generalized Lyapunov matrix equationApplied Numerical Mathematics, Vol. 181 | 1 Nov 2022 Cross Ref Balanced truncation for discrete time-delay systems via the interpretation of system energyJournal of the Franklin Institute, Vol. 359, No. 15 | 1 Oct 2022 Cross Ref New results of the IO iteration algorithm for solving Sylvester matrix equationJournal of the Franklin Institute, Vol. 359, No. 15 | 1 Oct 2022 Cross Ref Developing Kaczmarz method for solving Sylvester matrix equationsJournal of the Franklin Institute, Vol. 35 | 1 Sep 2022 Cross 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The rate of convergence of a matrix power seriesLinear Algebra and its Applications, Vol. 35 | 1 Feb 1981 Cross Ref An index theorem and Bendixson's negative criterion for certain differential equations of higher dimensionProceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 91, No. 1-2 | 14 November 2011 Cross Ref Berechnungsverfahren f�r stochastische FahrzeugschwingungenIngenieur-Archiv, Vol. 49, No. 3-4 | 1 May 1980 Cross Ref A CAD PROGRAM FOR SUBOPTIMAL LINEAR REGULATORSComputer Aided Design of Control Systems | 1 Jan 1980 Cross Ref ON THE APPLICATION OF NONLINEAR PROGRAMMING TO THE SOLUTION OF OPTIMAL OUTPUT-CONSTRAINED REGULATOR PROBLEMSControl Applications of Nonlinear Programming | 1 Jan 1980 Cross Ref A CAD Program for Suboptimal Linear RegulatorsIFAC Proceedings Volumes, Vol. 12, No. 7 | 1 Sep 1979 Cross Ref On the Application of Nonlinear Programming to the Solution of Optimal Output-constrained Regulator ProblemsIFAC Proceedings Volumes, Vol. 12, No. 2 | 1 Sep 1979 Cross Ref Covariance Analysis of Nonlinear Guideway-Vehicle-SystemsVehicle System Dynamics, Vol. 8, No. 2-3 | 27 July 2007 Cross Ref Author's replyIEEE Transactions on Automatic Control, Vol. 24, No. 4 | 1 Aug 1979 Cross Ref Algorithms for computation of optimal constrained output feedback for linear multivariable flight control systemsGuidance and Control Conference | 16 August 2012 Cross Ref An imbedded initialization of Newton's algorithm for matrix Riccati equationAutomatica, Vol. 14, No. 2 | 1 Mar 1978 Cross Ref Series solution of matrix Riccati equationInternational Journal of Control, Vol. 27, No. 3 | 19 April 2007 Cross Ref The numerical solution ofẊ = A_{1}X + XA_{2} + D, X(0) = CIEEE Transactions on Automatic Control, Vol. 22, No. 5 | 1 Oct 1977 Cross Ref Optimal approximation of transfer functions of linear dynamical systemsIEEE Transactions on Circuits and Systems, Vol. 24, No. 10 | 1 Oct 1977 Cross Ref Design algorithms for a sensitivity constrained suboptimal regulatorInternational Journal of Control, Vol. 25, No. 6 | 1 Jun 1977 Cross Ref Modern Aerospace SystemsAdvances in Theory and Applications | 1 Jan 1977 Cross Ref A stabilization algorithm for linear discrete constant systemsIEEE Transactions on Automatic Control, Vol. 21, No. 4 | 1 Aug 1976 Cross Ref Optimal regulation of stochastic linear systems with adjustable parameterIEEE Transactions on Automatic Control, Vol. 21, No. 1 | 1 Feb 1976 Cross Ref ORACLS-A modern control theory design package1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes | 1 Dec 1975 Cross Ref Explicit solutions of the matrix equationAX−XB=CRendiconti del Circolo Matematico di Palermo, Vol. 23, No. 2-3 | 1 May 1974 Cross Ref Gradient methods for optimal linear system reduction†International Journal of Control, Vol. 18, No. 4 | 2 May 2007 Cross Ref The use of model following methods to generate suboptimal feedback control†International Journal of Control, Vol. 17, No. 6 | 27 March 2007 Cross Ref Analysis of a discrete matrix Riccati equation of linear control and Kalman filteringJournal of Mathematical Analysis and Applications, Vol. 42, No. 1 | 1 Apr 1973 Cross Ref Approximation of discrete linear systemsInternational Journal of Control, Vol. 17, No. 3 | 27 March 2007 Cross Ref Design of optimal incomplete state feedback controllers for large linear constant systems5th Conference on Optimization Techniques Part I | 24 May 2005 Cross Ref A numerical algorithm for the computation of suboptimal controlsProceedings of the 1972 IEEE Conference on Decision and Control and 11th Symposium on Adaptive Processes | 1 Dec 1972 Cross Ref A Solution of the Bilinear Matrix Equation $AY + YB = - Q$G. KreisselmeierSIAM Journal on Applied Mathematics, Vol. 23, No. 3 | 12 July 2006AbstractPDF (406 KB)Comparison of numerical methods for solving Liapunov matrix equations†International Journal of Control, Vol. 15, No. 5 | 1 May 1972 Cross Ref Numerical solution of ATS + SA + Q = 0Information Sciences, Vol. 4, No. 1 | 1 Jan 1972 Cross Ref Numerical solution of the matrix equation AX + XAT+ B = 0IEEE Transactions on Automatic Control, Vol. 16, No. 3 | 1 Jun 1971 Cross Ref StabilityThe Theory of Linear Systems | 1 Jan 1971 Cross Ref Explicit Solutions of Linear Matrix EquationsPeter LancasterSIAM Review, Vol. 12, No. 4 | 18 July 2006AbstractPDF (1752 KB)A computational method for optimal control of a linear system by quadratic programming†International Journal of Control, Vol. 11, No. 6 | 16 January 2007 Cross Ref Solution of the Matrix Equations $AX + XB = - Q$ and $S^T X + XS = - Q$P. Chr. MüllerSIAM Journal on Applied Mathematics, Vol. 18, No. 3 | 1 August 2006AbstractPDF (362 KB)Smith-Type Methods for Balanced Truncation of Large Sparse SystemsDimension Reduction of Large-Scale Systems Cross Ref A portable subroutine library for solving linear control problems on distributed memory computersWorkshop on wide area networks and high performance computing Cross Ref Efficient approximate balanced truncation of general large-scale RLC systems via Krylov methodsProceedings of ASP-DAC/VLSI Design 2002. 7th Asia and South Pacific Design Automation Conference and 15h International Conference on VLSI Design Cross Ref A comparison of several methods for calculating the general functional matrix for linear systems†International Journal of Control, Vol. 10, No. 6 | 1 Dec 1969 Cross Ref Soluzione numerica dell'equazione matriciale ATX+XA=CCalcolo, Vol. 5, No. S2 | 1 Jun 1968 Cross Ref Volume 16, Issue 1| 1968SIAM Journal on Applied Mathematics1-254 History Submitted:14 April 1967Published online:12 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0116017Article page range:pp. 198-201ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics
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