LMI(线性矩阵不等式)工具箱

1、D The Canadian government pays little attention to Inuits education.C. Choose the words or expressions and complete the passage （选择最恰当的单词或词语完成短语）：（14分）Its six oclock on a cold Saturday morning. Zhang Hong doesnt want to 85 the warm bed. She has three classes awaiting-Chinese, maths and English.“I wi

2、sh I could sleep more,” says Zhang.The 12-year-old seventh grader from Beijing Guangqumen Secondary School must take an-hour-ride to get to the school for the extra courses（额外的课程） that spend her whole Saturday morning. On Sunday afternoon, she has music lessons from 3 p.m. to 7 p.m. During weekdays,

3、 Zhang 86 get up around five in the morning, and leave home by six. “My teacher suggests us eat an apple in the morning 87we wont feel sleepy,” she says.Chinese children face increasing pressures(压力 on study. Most Chinese parents believe high academic credentials (学历证书）mean a better school and a bri

4、ghter future. So they 88 their children to extra classes like music, English and maths to develop a special talent(才能, which later might be a stepping stone to a good school.Some parents make their children study 89 . First graders start to take classes for second grades, and so on. Therefore they c

5、an get an advantage in exams.According to Chinas Law on Compulsory Education(义务教育法, public primary and secondary schools do not require entrance exams. Students can enter the schools near their homes. However, a student can go to another desired school, if the student is 90 maths or English, or has

6、special talent in music and sports.Studies made by the China Youth and Children Research Center 91 that more than half of Chinese secondary school students study overtime and they do not get enough sleep. And more than 70 percent of primary and middle school students take tutoring classes(补习课, a hea

7、vy burden on the students.85. A sit on B stay in C get out of D lie in 该系统为H-inf 渐进稳定的，并且gammar87. A as B if C because D so that88. A send B invent C find D make89. A again B ahead C alone D along90. A poor at B good at C tired of D bad for91. A give B call C show D talkD.Read the passage and fill i

8、n the blanks with proper words (在短文的空格内填入适当的词, 使其内容通顺,没空格限填一词,首字母已给: (14分Several years ago, a famous TV series named Struggle (奋斗500this.width=500;" border=0> of Mi Lan in this TV series. Then she r_92_ a lot of applause(掌声 and praise. When Wang Luodan first went to Secondary Normal School （

9、师范中专）, she began to show her ability in art and literature(文学. She was the o 93 one in her school who could play the drums, besides playing the piano and dancing well. “I felt that I was very cool at that time.” Wang said.In 2001, Wang Luodan entered the Beijing Film Academy(学院, learning performance

10、. She worked hard as a c   student and had great patience. When her classmates became famous, she was not w 95 or disappointed.Her first TV series was Butterfly in the Air. Because of her sweet appearance, she was chosen for the role of Shan Juan in the TV series Sun Shining like Blossom. In or

11、der to play the role well, Wang cut her long h 96 and missed the chance to appear in the movie Qinghong. Last year, The TV series My youthfulness was very p 97 . Wang Luodan played Qian Xiaoyang, a confident, lovely and garrulous（喋喋不休的）country girl. Now many of Qian Xiaoyangs classic(经典的 words are v

12、ery popular on the Internet such as “The time is too slim as well as the slot of fingers is too broad. (时间太瘦，指缝太宽。” Wang Luodan is an ambitious a 98 , she will achieve more in the future.500this.width=500;" border=0>EAnswer the questions (根据短文内容回答下列问题：（14分） BY Liz Davies Do you have the

13、 dedication(LMI进行求解，验证论文结果。3 a.m.? Do you have the courage to climb mountains? Do you have a clear head to stay calm in an emergency(危急? Would you know what to do if somebody broke their leg?girl from California in America, can answer yes to all those questions. She joined the Marine Search and Resc

14、ue Team when she was only 14 years old-the youngest age you can do this. 首先我们要用setlmis(had to be trained for 60 hours to learnabout first aid, climbing, map reading and rescue techniques ( 技术 before she began to help others . But she gained a lot from her teacher and teammates. T he training gave he

15、r the confidence to do the job. Now she is one of 20 youth volunteers ( 志愿者 in the rescue team whose mo tto( 座右铭 is "Any time, any place, any weather." They are often called out in the middle of the night to help people who have got into trouble in the wild countryside of California . So s

16、he usually had to stay up and got up early the next morning. 接下来，我们就要设定矩阵变量了。采用函数为lmivar 语法：X = lmivar(type,struct type=1: 定义块对角的对称矩阵。 每一个对角块或者是全矩阵<任意对称矩阵>，标量<单位矩阵的乘积>，或者是零阵。如果X有R个对角块，那么后面这个struct就应该是一个Rx2阶的的矩阵，在此矩阵中，struct(r,1表示第r个块的大小，struct(r,2 表示第r个块的类型<1-全矩阵，0-标量，-1-零阵）。比如一个

17、矩阵有两个对角块，其中一个是2x2的全对称矩阵，第二个是1x1的一个标量，那么该矩阵变量应该表示为X = lmivar(1, 2 1; 1 0 。type=2: mxn阶的矩阵，只需要写作struct = m,n即可。type=3: 其它类型。针对类型3，X的每一个条目（each entry of X）被定义为0或者是+(-xn，此处xn代表了第n个决策变量。那么针对我们的例子，我们如此定义变量：% Q is a symmetric matrix, has a block size of 2 and this block is symmetric Q = lmivar(1, 2 1;

18、% S1 a symmeric matrix, size 2 S1 = lmivar(1, 2 1;% S2 is 1 by 1 matrixS2 = lmivar(1, 1 0;% Type of 2, size 1 by 2 M = lmivar(2, 1 2;定义完成变量之后，我们就该用lmiterm来描述LMI中的每一个项了。Matlab的官方文档提示我们，如果要描述一个LMI只需要描述上三角或者下三角元素就可以了，否则会描述成另一个LMI。When describing an LMI with several blocks, remember to specify only the

19、terms in the blocks on or below the diagonal (or equivalently, only the terms in blocks on or above the diagonal.语法为：lmiterm(termID,A,B,flagtermID是一个四维整数向量，来表示该项的位置和包含了哪些矩阵变量。termID(1可以为+p或者-p，+p代表了这个项位于第p个线性矩阵不等式的左边，-p代表了这个项位于第p个线性矩阵不等式的右边。注意：按照惯例来讲，左边通常指较小的那边。termID(2:3:1、对于外部变量来说，取值为0,0;2、对于左边或者右

20、边的内部变量来说，如果该项在(i,j位置，取值i,jtermID(4:1、对于外部变量，取值为02、对于A*X*B，取值X3、对于A*X'*B，取值-Xflag(可选，值为s）:因为：(A*X*B + (A*X*BT = A*X*B + B'*X'*A'，所以采用s来进行简写。比如：针对A*X + X'*A'我们采用笨方法：lmiterm(1 1 1 X,A,1 lmiterm(1 1 1 -X,1,A'那么简写就是lmiterm(1 1 1 X,A,1,'s'接下来我们就看该论文中的算例吧：(1,1位置是-Q+Bd*S2

21、*Bd'+Ad*S1*Ad'我们应该表示为：% pos in (1, 1lmiterm(1 1 1 Q, -1, 1;lmiterm(1 1 1 S2, Bd, Bd'lmiterm(1 1 1 S1, Ad, Ad'其它位置仿照写就行了，不懂了多看帮助文档。把每一个项都定义以后，要记得lmis = getlmis;tmin, feas = feasp(lmisgetlmis:是在完成定义变量和项之后，LMI系统的内部表示就可以通过此命令获得（After completing the description of a given LMI system with

22、lmivar and lmiterm, its internal representation lmisys is obtained with the command）。feasp是调用feasp求解器，看有没有可行解。feas就是可行解。下面我把代码贴上去，那些常数矩阵都在此源程序中定义了。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

23、LMI systemsetlmis(;% 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 matrixS2 = lmivar(1, 1 0;% Type of 2, size 1 by 2 M = lmivar(2, 1 2;% Q, S1, S2 > 0lmiterm(-2 1 1 Q, 1, 1;lmiterm(-3 1 1 S1, 1, 1;lmiterm(-4 1 1 S2, 1, 1;% pos in (1, 1lmiterm(1 1 1 Q, -1, 1;lm