.TH ssrand 1 "April 1993" "Scilab Group" "Scilab Function"
.so man1/sci.an
.SH NAME
ssrand - random system generator
.SH CALLING SEQUENCE
.nf
sl=ssrand(nout,nin,nstate)
[sl,U]=ssrand(nout,nin,nstate,flag)
.fi
.SH PARAMETERS
.TP 10
nout
: integer (number of output)
.TP
nin
: integer (number of input)
.TP
nstate
: integer (dimension of state-space)
.TP
flag
: list made of one character string and one or several integers
.TP
sl
: list (\fVsyslin\fR list)
.TP
U square \fV(nstate x nstate)\fR nonsingular matrix
.SH DESCRIPTION
\fVsl=ssrand(nout,nin,nstate)\fR returns a random strictly proper 
(\fVD=0\fR) state-space system of size \fV[nout,nint]\fR represented 
by a \fVsyslin\fR list and with \fVnstate\fR state variables.
.LP
\fV[sl,U]=ssrand(nout,nin,nstate,flag)\fR returns a test linear system
with given properties specified by \fVflag\fR.
\fVflag\fR can be one of the following:
.nf
flag=list('co',dim_cont_subs)  
flag=list('uo',dim_unobs_subs)
flag=list('ncno',dim_cno,dim_ncno,dim_co,dim_nco)
flag=list('st',dim_cont_subs,dim_stab_subs,dim_stab0)  
flag=list('dt',dim_inst_unob,dim_instb0,dim_unobs)
flag=list('on',nr,ng,ng0,nv,rk)
flag=list('ui',nw,nwu,nwui,nwuis,rk)
.fi
The complete description of the \fVSys\fR is given in the code
of the \fVssrand\fR function (in \fVSCIDIR/macros/util\fR).
For example with \fVflag=list('co',dim_cont_subs)\fR a non-controllable
system is return and \fVdim_cont_subs\fR is the dimension
of the controllable subspace of \fVSys\fR.
The character strings \fV'co','uo','ncno','st','dt','on','ui'\fR
stand for "controllable", "unobservable", "non-controllable-non-observable",
"stabilizable","detectable","output-nulling","unknown-input".
.SH EXAMPLE
.nf
//flag=list('st',dim_cont_subs,dim_stab_subs,dim_stab0)  
//dim_cont_subs<=dim_stab_subs<=dim_stab0  
//pair (A,B) U-similar to:
//    [*,*,*,*;     [*;    
//    [0,s,*,*;     [0;
//A=  [0,0,i,*;   B=[0;
//    [0,0,0,u]     [0]
//     
// (A11,B1) controllable  s=stable matrix i=neutral matrix u=unstsble matrix
// [Sl,U]=ssrand(2,3,8,list('st',2,5,5));
// w=ss2ss(Sl,inv(U)) //undo the random change of basis => form as above
// [n,nc,u,sl]=st_ility(Sl);n,nc
.fi
.SH SEE ALSO:
syslin