Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`LinearSystems`
systemoperation  |
| system | |
Examples
(1)
Basic Examples
(1)
In[1]:=
system1={{x1,x2,x3},{u1,w1,u2,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,0,1,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{1,3},{1,2},{1,3},{2,4},{1,2},{3,4}};
In[2]:=
 | systemoperation |
Active | a1 | a2 | |||||||
Type | s1 | s2 | s3 | c1 | d1 | c2 | d2 | ||
names | x1 | x2 | x3 | u1 | w1 | u2 | w2 | ||
s1 | x1 | -1 | θ1 | 0 | 0 | 0 | 0 | 1 | |
s2 | x2 | -2 | -1 | 1 | 1 | 1 | 1 | 0 | |
s3 | x3 | -1 | -θ2 | -3 | -1 | 1 | 1 | 1 | |
a1 | m1 | y1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
a2 | m2 | y2 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
c1 | z1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
c2 | z2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
Out[2]=
{{x1,x2,x3},{u1,w1,u2,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,0,1,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{1,3},{1,2},{1,3},{2,4},{1,2},{3,4}}
In[3]:=
system2=
[system1,{"Organize and View"}]
 | systemoperation |
Active | a1 | a2 | |||||||
Type | s1 | s2 | s3 | c1 | c2 | d1 | d2 | ||
names | x1 | x2 | x3 | u1 | u2 | w1 | w2 | ||
s1 | x1 | -1 | θ1 | 0 | 0 | 0 | 0 | 1 | |
s2 | x2 | -2 | -1 | 1 | 1 | 1 | 1 | 0 | |
s3 | x3 | -1 | -θ2 | -3 | -1 | 1 | 1 | 1 | |
a1 | m1 | y1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
a2 | m2 | y2 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
c1 | z1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
c2 | z2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
Out[3]=
{{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,1,0,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4}}
In[4]:=
system3=
[system2,{"Drop active inputs",{u1}}]
| systemoperation |
Out[4]=
{{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,1,0,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{2},{1,2},{1,2},{3,4},{1,2},{3,4}}
In[5]:=
| systemoperation |
Active | a1 | ||||||||
Type | s1 | s2 | s3 | c1 | c2 | d1 | d2 | ||
names | x1 | x2 | x3 | u1 | u2 | w1 | w2 | ||
s1 | x1 | -1 | θ1 | 0 | 0 | 0 | 0 | 1 | |
s2 | x2 | -2 | -1 | 1 | 1 | 1 | 1 | 0 | |
s3 | x3 | -1 | -θ2 | -3 | -1 | 1 | 1 | 1 | |
a1 | m1 | y1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
a2 | m2 | y2 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
c1 | z1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
c2 | z2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
Out[5]=
{{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,1,0,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{2},{1,2},{1,2},{3,4},{1,2},{3,4}}
In[6]:=
| systemoperation |
 | systemoperation |
Active | a2 | a1 | |||||||
Type | s1 | s2 | s3 | c1 | c2 | d1 | d2 | ||
names | x1 | x2 | x3 | u1 | u2 | w1 | w2 | ||
s1 | x1 | -1 | θ1 | 0 | 0 | 0 | 0 | 1 | |
s2 | x2 | -2 | -1 | 1 | 1 | 1 | 1 | 0 | |
s3 | x3 | -1 | -θ2 | -3 | -1 | 1 | 1 | 1 | |
a1 | m1 | y1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
a2 | m2 | y2 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
c1 | z1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
c2 | z2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
Out[6]=
{{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,1,0,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{2,1},{1,2},{1,2},{3,4},{1,2},{3,4}}
In[7]:=
| systemoperation |
| systemoperation |
Active | a2 | a1 | |||||||
Type | s1 | s2 | s3 | c1 | c2 | d1 | d2 | ||
names | x1 | x2 | x3 | u1 | u2 | w1 | w2 | ||
s1 | x1 | -1 | θ1 | 0 | 0 | 0 | 0 | 1 | |
s2 | x2 | -2 | -1 | 1 | 1 | 1 | 1 | 0 | |
s3 | x3 | -1 | -θ2 | -3 | -1 | 1 | 1 | 1 | |
a1 | m1 | y1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
a2 | m2 | y2 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
c1 | z1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
c2 | z2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
Out[7]=
{{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,1,0,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{2,1},{1,2},{1,2},{3,4},{1,2},{3,4}}
In[8]:=
| systemoperation |
| systemoperation |
Active | a1 | a2 | |||||||
Type | s1 | s2 | s3 | c1 | c2 | d1 | d2 | ||
names | x1 | x2 | x3 | u1 | u2 | w1 | w2 | ||
s1 | x1 | -1 | θ1 | 0 | 0 | 0 | 0 | 1 | |
s2 | x2 | -2 | -1 | 1 | 1 | 1 | 1 | 0 | |
s3 | x3 | -1 | -θ2 | -3 | -1 | 1 | 1 | 1 | |
a1 | m1 | y1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
a2 | m2 | y2 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
c1 | z1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
c2 | z2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
Out[8]=
{{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,1,0,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4}}
In[9]:=
| systemoperation |
| systemoperation |
Active | a1 | a2 | |||||||
Type | s1 | s2 | s3 | c1 | c2 | d1 | d2 | ||
names | x1 | x2 | x3 | u1 | u2 | w1 | w2 | ||
s1 | x1 | -1 | θ1 | 0 | 0 | 0 | 0 | 1 | |
s2 | x2 | -2 | -1 | 1 | 1 | 1 | 1 | 0 | |
s3 | x3 | -1 | -θ2 | -3 | -1 | 1 | 1 | 1 | |
m1 | y1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | |
m2 | y2 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | |
a1 | c1 | z1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
a2 | c2 | z2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
Out[9]=
{{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,θ1,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-θ2,-3,-1,1,1,1},{1,0,0,0,1,0,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0}},{1,2},{3,4},{1,2},{3,4},{1,2},{3,4}}
In[10]:=
| systemoperation |
| systemoperation |
Active | a1 | ||||||
Type | s1 | s2 | s3 | c1 | d1 | ||
names | x1 | x2 | x3 | u2 | w1 | ||
s1 | x1 | -1 | θ1 | 0 | 0 | 0 | |
s2 | x2 | -2 | -1 | 1 | 1 | 1 | |
s3 | x3 | -1 | -θ2 | -3 | 1 | 1 | |
a1 | m1 | y1 | 1 | 0 | 0 | 1 | 0 |
a2 | m2 | y2 | 0 | 1 | 0 | 0 | 0 |
c1 | z1 | 1 | 0 | 0 | 0 | 0 | |
c2 | z2 | 0 | 1 | 0 | 0 | 0 |
Out[10]=
{{x1,x2,x3},{u2,w1},{y1,y2,z1,z2},{{-1,θ1,0,0,0},{-2,-1,1,1,1},{-1,-θ2,-3,1,1},{1,0,0,1,0},{0,1,0,0,0},{1,0,0,0,0},{0,1,0,0,0}},{1},{1,2},{1},{2},{1,2},{3,4}}
In[11]:=
| systemoperation |
| systemoperation |
State transformation is xold = transformation.xnew
Active | a1 | a2 | |||||||
Type | s1 | s2 | s3 | c1 | c2 | d1 | d2 | ||
names | x11 | x21 | x31 | u1 | u2 | w1 | w2 | ||
s1 | x11 | -1 | 0 | 2θ1 | 0 | 0 | 0 | 1 | |
s2 | x21 | 1 | -3 | 2θ2 | 1 | -1 | -1 | -1 | |
s3 | x31 | -1 | - 1 2 | -1 | 1 2 | 1 2 | 1 2 | 0 | |
a1 | m1 | y1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
a2 | m2 | y2 | 0 | 0 | 2 | 0 | 0 | 0 | 1 |
c1 | z1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
c2 | z2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 |
Out[11]=
{x11,x21,x31},{u1,u2,w1,w2},{y1,y2,z1,z2},{-1,0,2θ1,0,0,0,1},{1,-3,2θ2,1,-1,-1,-1},-1,-,-1,,,,0,{1,0,0,0,1,0,0},{0,0,2,0,0,0,1},{1,0,0,0,0,0,0},{0,0,2,0,0,0,0},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4}
1
2
1
2
1
2
1
2
 |
|