Kitagawa, An Algorithm for Solving the Matrix Equation X = F X F' + S, International Journal of Control, Vol. 25, No. 5, p745–753 (1977).
R. H. Bartels and G. W. Stewart, Algorithm 432: Solution of the matrix equation AX + XB = C, Comm. ACM, 15 (1972), p820-826.
J. Hamilton (1994), Time Series Analysis, equations 10.2.13 and 10.2.18. Princeton University Press.
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Online solver for arbitrary sized matrices.[ลิงก์เสีย]
ตุลาคม 25, 2021
สมการเล, ยป, นอฟ, บทความน, างอ, งคร, สต, กราช, คร, สต, ทศวรรษ, คร, สต, ศตวรรษ, งเป, นสาระสำค, ญของเน, อหา, งก, ามภาษา, ในบทความน, ไว, ให, านและผ, วมแก, ไขบทความศ, กษาเพ, มเต, มโดยสะดวก, เน, องจากว, เด, ยภาษาไทยย, งไม, บทความด, งกล, าว, กระน, ควรร, บสร, างเป, น. bthkhwamnixangxingkhristskrach khristthswrrs khriststwrrs sungepnsarasakhykhxngenuxha lingkkhamphasa inbthkhwamni miiwihphuxanaelaphurwmaekikhbthkhwamsuksaephimetimodysadwk enuxngcakwikiphiediyphasaithyyngimmibthkhwamdngklaw krann khwrribsrangepnbthkhwamodyerwthisudinthvsdirabbkhwbkhumsmkareliypunxfimtxenuxng xngkvs discrete Lyapunov equation khuxsmkarinrupaebb A X A H X Q 0 displaystyle AXA H X Q 0 odythi Q displaystyle Q khux emthriksexrmiechiyn Hermitian matrix aela A H displaystyle A H khux emthriksslbepliynsngyukh conjugate transpose khxng A displaystyle A inkhnathi smkareliypunxftxenuxng xngkvs continuous Lyapunov equation khuxsmkarinrupaebb A X X A H Q 0 displaystyle AX XA H Q 0 smkareliypunxfmkthukichinhlaysakhakhxngthvsdirabbkhwbkhumechn inkarwiekhraahesthiyrphaph aelakarkhwbkhumaebbehmaasmthisud optimal control odychuxkhxngsmkarnitngtamchuxkhxng xelksanedxr mikhaxilolwich eliypunxf nkkhnitsastrchawrsesiy 6 mithunayn kh s 1857 3 phvscikayn kh s 1918 enuxha 1 karprayuktichkbkarwiekhraahesthiyrphaph 2 aengmuminkarkhanwn 3 phltxbechingwiekhraah 4 duephim 5 xangxing 6 aehlngkhxmulxunkarprayuktichkbkarwiekhraahesthiyrphaph aekikhinthinierakahndih A P Q R n n displaystyle A P Q in mathbb R n times n aela P displaystyle P aela Q displaystyle Q epnemthrikssmmatr sylksn P gt 0 displaystyle P gt 0 hmaythuxwa P displaystyle P khux emthriksbwkaennxn Positive definite matrix thvsdiesthiyrphaphkrniewlatxenuxng thami P gt 0 displaystyle P gt 0 aela Q gt 0 displaystyle Q gt 0 thisamarththaih A T P P A Q 0 displaystyle A T P PA Q 0 epncringaelw rabbechingesn linear system x A x displaystyle dot x Ax esthiyrphaphwngkwangechingesnkakb globally asymptotically stable odythismkarkalngsxng V z z T P z displaystyle V z z T Pz nncaniyamepn fngkchneliypunxf Lyapunov function sungichinkartwrcsxbesthiyrphaphkhxngrabbthvsdiesthiyrphaphkrniewlatxenuxngimtxenuxng thami P gt 0 displaystyle P gt 0 aela Q gt 0 displaystyle Q gt 0 thisamarththaih A T P A P Q 0 displaystyle A T PA P Q 0 epncringaelw rabbechingesn x t 1 A x t displaystyle x t 1 Ax t esthiyrphaphwngkwangechingesnkakb aela z T P z displaystyle z T Pz nnkhuxfngkchneliypunxfaengmuminkarkhanwn aekikhsmkareliypunxfimtxenuxngsamarthich swnetimetmchur Schur complement inkarkhanwniddngkhntxnwithithiaesdngkhanglangni X 1 A A H X Q 0 displaystyle begin bmatrix X 1 amp A A H amp X Q end bmatrix 0 sungsmmulkb X X A A H X X Q 0 displaystyle begin bmatrix X amp XA A H X amp X Q end bmatrix 0 nxkcakniyngmisxftaewrechphaathangiheluxkichinkarkhanwnsmkareliypunxf odyinkrnismkareliypunxfimtxenuxng withikarkhxngchurodykitakawa Schur method of Kitagawa 1 mkepnthiniym inkhnathikrnismkareliypunxftxenuxngwithikarkhxng barethl aela chwars 2 samarthichidechnknphltxbechingwiekhraah aekikherasamarthhaphltxbechingwiekhraah analytic solution sahrbkrnismkareliypunxfimtxenuxng odnniyamih vec A displaystyle text vec A epntwdaeninkarthithakareriyngsxnkhxlmnkhxngemthriksA displaystyle A aelaniyam kron A B displaystyle text kron A B epn phlkhunokhnenkekxr Kronecker product rahwang A displaystyle A aela B displaystyle B aelaodykarichphlcak vec A B C kron C T A vec B displaystyle text vec ABC text kron C T A text vec B erasamarthich I kron A A vec X vec Q displaystyle I text kron A A text vec X text vec Q emux I displaystyle I khux emthriksexklksnthi conformable 3 caknnerasamarthaeksmkarsahrbhakhakhxng vec X displaystyle text vec X odykarhaemthriksphkphnhruxkaraeksmkarechingesn odyinkaridmasungkha X displaystyle X txngmikarprbkhnadkhxng vec X displaystyle text vec X xyangehmaasmdwyduephim aekikhfngkchneliypunxf smkarsilewsetxr smkarrikkhatikechingphuchkhnit Algebraic Riccati equation thvsdirabbkhwbkhumxangxing aekikh Kitagawa An Algorithm for Solving the Matrix Equation X F X F S International Journal of Control Vol 25 No 5 p745 753 1977 R H Bartels and G W Stewart Algorithm 432 Solution of the matrix equation AX XB C Comm ACM 15 1972 p820 826 J Hamilton 1994 Time Series Analysis equations 10 2 13 and 10 2 18 Princeton University Press aehlngkhxmulxun aekikhOnline solver for arbitrary sized matrices lingkesiy ekhathungcak https th wikipedia org w index php title smkareliypunxf amp oldid 9668084, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,
