矩阵方程AXB=C的matlab程序 急！！！！哪位高手会用matlab解矩阵方程AXB+CXD=...
matlab \u6c42 XA-AX=B \u8fd9\u6837\u7684\u77e9\u9635\u65b9\u7a0b\uff0c\uff08\u5176\u4e2dA\u3001B\u5df2\u77e5\uff0c\u6c42X\uff09\u3002\u82e5\u6709\u529e\u6cd5\u6c42\u5341\u5206\u611f\u8c22\uff01\uff01\uff01\u6709\u5173\u8fd9\u79cd\u77e9\u9635\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u6709\u4e00\u4e0b\u4e24\u7c7b
Standard CT Lyapunov: AX +XA^T =C
Standard CT Sylvester: AX −XB =C
Matlab\u6709lyap\u51fd\u6570\u89e3\u6b64\u65b9\u7a0b\u3002\u8be6\u60c5\u8bf7\u89c1 http://www.mathworks.com/help/control/ref/lyap.html
\u8fd9\u4e2a\u7f51\u9875\u4e5f\u7ed9\u51fa\u4e86\u4e00\u4e9b\u6709\u5173\u8fd9\u7c7b\u65b9\u7a0b\u7684\u8bba\u6587\u3002
\u5047\u8bbeA\u4e0d\u4e00\u5b9a\u662f\u5bf9\u79f0\u7684\uff0c\u4f60\u53ef\u4ee5\u7528 X = lyap(A,A.',-B)\u6c42\u89e3\u3002
\u5148\u628a\u65b9\u7a0b\u53d8\u578b\u6210\u5982\u4e0b\u5f62\u5f0f\uff1a
aX+Xb=-c
\u8fd9\u4e2a\u662fSylvester\u65b9\u7a0b,\u5176\u4e2d\u7684a,b,c\u4f60\u81ea\u5df1\u8f6c\u6362\u5427\uff0c\u56e0\u4e3a\u6709\u77e9\u9635\u9006\u7684\u7b26\u53f7\uff0c\u6211\u4e0d\u597d\u8868\u793a\u3002\uff08\u6ce8\u610fc\u524d\u9762\u6709\u4e2a\u8d1f\u53f7\uff09
\u7136\u540e\u4f60\u7528MATLAB\u81ea\u5e26\u7684\u5de5\u5177\u7bb1\u4e2d\u7684lyap()\u51fd\u6570\u6c42\u89e3\u3002\u547d\u4ee4\u8f93\u5165\u5982\u4e0b\uff1a
X=lyap(a,b,c)
AX=B的解是A左除B,即 X=A\B
XA=B的解是A右除B, 即X=B/A。
具体到这里：A,B都是可逆矩阵，X=(A\C)/B
C=cross(A,B) %A叉乘B=C
pinv（kron（B’，A））*C（：）；
绛旓細鍦matlab涓紝濡傛灉A鏄彲閫鐭╅樀 AX=B鐨勮В鏄疉宸﹂櫎B,鍗 X=A\B XA=B鐨勮В鏄疉鍙抽櫎B, 鍗砐=B/A銆傚叿浣撳埌杩欓噷锛欰,B閮芥槸鍙嗙煩闃碉紝X=(A\C)/B
绛旓細鐪嬭捣鏉ヨВ娉曟槸瀵圭殑銆備綘鍙互鐢ㄥ緱鍒扮殑X杩涜楠岃瘉锛氱湅鐪婣*X*B=C鏄惁鎴愮珛銆傚鏋滈獙璇佹纭紝閭ｈ偗瀹氬氨涓嶆槸鐭╅樀璁＄畻鐨勯棶棰樹簡銆
绛旓細1銆佸姞鍑忔硶鐨勫懡浠ゅ緢绠鍗曪紝鐩存帴鐢ㄥ姞鎴栬呭噺鍙峰氨鍙互浜嗐傚锛c=a+bd=a-b銆2銆佷竴鑸箻娉曪細c=a*b,瑕佹眰a鐨勫垪鏁扮瓑浜巄鐨勮鏁般傚鏋渁,b鏄竴鑸殑鍚戦噺锛屽a=[1,2,3] b=[3,4,5]鐐圭Н锛歞ot(a,b), 鍙夌Н锛歝ross锛坅,b)鍗风Н锛歝onv(a,b)銆3銆亁=a\b濡傛灉ax=b锛屽垯 x=a\b鏄鐭╅樀鏂圭▼鐨瑙ｃ...
绛旓細涓ゅ紡鐩稿姞鍙緱锛孉=(C+D)/2 鎯冲噺涓猴細B=(C-D)/2
绛旓細r = rank(A);s = rank([A C]);if r==s X = A\C; %姝ゆ椂鏂圭▼缁勬湁瑙.else error('鎵缁欐柟绋嬫棤瑙')end
绛旓細AX=b;瑙ｆ柟绋嬬粍濡備笅锛MATLAB鍒╃敤鐭╅樀姹傜嚎鎬ф柟绋嬬粍 MATLAB鍒╃敤鐭╅樀姹傜嚎鎬ф柟绋嬬粍 4 瓒呭畾鏂圭▼缁 瓒呭畾鏂圭▼缁勬槸鎸鏂圭▼鐨涓暟澶т簬鏈煡鏁扮殑涓暟鐨勭嚎鎬ф柟绋嬬粍锛岄氬父鍙湁杩戜技鐨勬渶灏忎簩涔樿В銆Matlab璇█鏍煎紡锛歑=pinv(A)*b 瑙ｄ笅闈㈡柟绋嬬粍锛歁ATLAB鍒╃敤鐭╅樀姹傜嚎鎬ф柟绋嬬粍 MATLAB鍒╃敤鐭╅樀姹傜嚎鎬ф柟绋嬬粍 ...
绛旓細鍏堝皢xP=0涓よ竟鍙栬浆缃紝寰桺'x'=0,姹傚嚭x'鍐嶈浆缃洖鏉ユ眰鍑簒.褰鐭╅樀鏂圭▼P'x'=0,rank(P)=r<n鏃,鍗砅鏄寮傜殑锛岃繖鏃舵柟绋嬫湁鏃犵┓澶氫釜瑙,鐢MATLAB鍙眰鍑哄畠鐨勪竴涓熀鏈В绯伙紝 鍩烘湰瑙ｇ郴鐨勭嚎鎬х粍鍚堝氨鏄畠鐨勯氳В锛堜竴鑸В锛夎屾眰鍩烘湰瑙ｇ郴鐢matlab 涓鐨勫懡浠 x=null(P', r )鍗冲彲.鍏朵腑:r=rank(P)....
绛旓細Ax = 0 A = [A00 - 1,A10;A01,R*A2 - 1]x = (pi0,pi1)(T)浣犺繕鏈変竴涓害鏉熸潯浠讹紝瀵瑰惂锛1=pi0*e+pi1*inv(I-R)*e;杩欑浉褰撲簬绾挎鏂圭▼缁勭殑绗笁琛屻傛墍浠ョ浉褰撲簬锛// 浠ｇ爜濡備笅 A = [A00 - 1,A10;A01,R*A2 - 1;e,*inv(I-R)*e];b = [0;0;1];x = A\b;// Matla...
绛旓細matlab涓瑙ｆ柟绋嬬粍杩樻槸寰堟柟渚跨殑锛屼緥濡傦紝瀵逛簬浠ｆ暟鏂圭▼缁凙x=b(A涓虹郴鏁扮煩闃碉紝闈炲寮)鐨勬眰瑙ｏ紝MATLAB涓鏈変袱绉嶆柟娉曪細(1)x=inv(A)*b 鈥 閲囩敤姹傞嗚繍绠楄В鏂圭▼缁勶紱(2)x=A\B 鈥 閲囩敤宸﹂櫎杩愮畻瑙ｆ柟绋嬬粍 PS锛氫娇鐢ㄥ乏闄ょ殑杩愮畻鏁堢巼瑕佹瘮姹傞鐭╅樀鐨鏁堢巼楂樺緢澶殈渚:x1+2x2=8 2x1+3x2=13 >>A=[1,2;2,3...
绛旓細1. 璁Ax = b锛屾眰x锛岋紙x鍜宐閮芥槸鍚戦噺锛夊垯锛歺 = A\b 灏辫繖涔堢畝鍗曘傛兂涓嶅嚭鏇村鏉傜殑鏂规硶浜嗐2. 浣犱笂闈㈢殑鐪嬭捣鏉ユ槸涓綈娆℃柟绋嬶紝浣嗘槸鍥犱负b1 b2 b3宸茬煡锛屽彲浠ョЩ鍒扮瓑鍙峰彟涓杈癸紱鍐嶆妸V3=V4鏁寸悊鍒鐭╅樀鏂圭▼閲屾垨鑰呭共鑴嗕粠鏂圭▼涓幓鎺塚4锛屽氨鍙互鐢ㄤ笂闈㈡柟娉曡В浜嗐
