matlablmi工具箱使用教程算例及论文原文.doc

LMI工具箱使用教程算例 算 例 是 论 文 ： H∞ state feedback control for generalized continuous/discrete time-delay system 中第三部分里面的一个例子。论 文原文附在后面。 算例程序如下： A = [2 1; 0 1]; Ad = [0.2 0.1; 0 0.1]; B1 = [0.1 0.1]; B2 = [1 1]; Bd = [0.1 0.1]; C = [1, 1]; Cd = [0.1, 0.1]; D11 = 0.1; D12 = 1; Dd = 0.1; gammar = 1; % Initial a LMI system setlmis([]); % Define Variables % Q is a symmetric matrix, has a block size of 2 and this block is symmetric Q = lmivar(1, [2 1]); % S1 a symmeric matrix, size 2 S1 = lmivar(1, [2 1]); % S2 is 1 by 1 matrix S2 = lmivar(1, [1 0]); % Type of 2, size 1 by 2 M = lmivar(2, [1 2]); % Q, S1, S2 0 QN = newlmi; lmiterm([-QN 1 1 Q], 1, 1); S1N = newlmi; lmiterm([-S1N 1 1 S1], 1, 1); S2N = newlmi; lmiterm([-S2N 1 1 S2], 1, 1); MAllN = newlmi; % pos in (1, 1) lmiterm([MAllN 1 1 Q], -1, 1); lmiterm([MAllN 1 1 S2], Bd, Bd); lmiterm([MAllN 1 1 S1], Ad, Ad); % pos (1, 2) lmiterm([MAllN 1 2 Q], A, 1); lmiterm([MAllN 1 2 M], B2, 1); % pos(1, 3) lmiterm([MAllN 1 3 0], B1); % pos(1, 4) lmiterm([MAllN 1 4 S2], Bd, Dd); lmiterm([MAllN 1 4 S1], Ad, Cd); % pos(2, 2) lmiterm([MAllN 2 2 Q], -1, 1); % pos(2, 4) lmiterm([MAllN 2 4 Q], 1, C); lmiterm([MAllN 2 4 -M], 1, D12); % pos(2, 5) lmiterm([MAllN 2 5 -M], 1, 1); % pos(2, 6) lmiterm([MAllN 2 6 Q], 1, 1); % pos(3, 3) lmiterm([MAllN 3 3 0], -(gammar^2)); % pos(3, 4) lmiterm([MAllN 3 4 0], D11); % pos(4, 4) lmiterm([MAllN 4 4 0], -1); lmiterm([MAllN 4 4 S1], Cd, Cd); lmiterm([MAllN 4 4 S2], Dd, Dd); lmiterm([MAllN 5 5 S2], -1, 1); lmiterm([MAllN 6 6 S1], -1, 1); lmis = getlmis; [tmin, feas] = feasp(lmis) 运行上述程序后，在命令窗口 （1）输入：Q = dec2mat(lmis, feas, Q) 得出： Q = 1.9253 -2.2338 -2.2338 9.1054 （2）输入：P = Q^-1 P = 0.7261 0.1781 0.1781 0.1535 （3）输入：S1 = dec2mat(lmis, feas, S1) 得出： S1 = 16.0928 -14.9665 -14.9665 30.3214 输入：R1=S1^-1 得出： R1 = 0.1149 0.0567 0.0567 0.0610 （４）输入：S2 = dec2mat(lmis, feas, S2) 得出： S2 = 16.0495 输入：R2=S2^-1 得出： R2 = 0.0623 （5）输入：M = dec2mat(lmis, feas, M) 得出： M = -0.2279 -6.2240 （6）输入：K=M*P 得出： K = -1.2741 -0.9961 与论文中结果