Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`LinearSystems`
calculaterelativedegree |
| {vectorrelativedegree,relativedegrees,highfrequencygain}=calculaterelativedegree[a,b,c,d] a b c d vectorrelativedegree relativedegrees highfrequencygain | |
Examples
(1)
Basic Examples
(1)
In[1]:=
system={{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,2,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-2,-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}},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4}};
In[2]:=
n=Length[system〚1〛];p=Length[system〚5〛];m=Length[system〚6〛];
In[3]:=
{vectorrelativedegree,relativedegrees,highfrequencygain}=
[system〚4〛〚1;;n,1;;n〛,system〚4〛〚1;;n,n+1;;n+p〛,system〚4〛〚n+1;;n+m,1;;n〛,system〚4〛〚n+1;;n+m,n+1;;n+p〛]
 | calculaterelativedegree |
Out[3]=
{False,{2,1},{{2,2},{1,1}}}
In[4]:=
system=
[{{1,2},{2,-1}}]
| gainsystem |
Out[4]=
{{},{tempinput1,tempinput2},{tempoutput1,tempoutput2},{{1,2},{2,-1}},{1,2},{1,2},{1,2},{},{1,2},{}}
In[5]:=
n=Length[system〚1〛];p=Length[system〚5〛];m=Length[system〚6〛];
In[6]:=
{vectorrelativedegree,relativedegrees,highfrequencygain}=
[system〚4〛〚1;;n,1;;n〛,system〚4〛〚1;;n,n+1;;n+p〛,system〚4〛〚n+1;;n+m,1;;n〛,system〚4〛〚n+1;;n+m,n+1;;n+p〛]
| calculaterelativedegree |
Out[6]=
{True,{0,0},{{1,2},{2,-1}}}
 |
|
""