Estimates the initial state of a discrete-time system
X0 = inistate(SYS,Y,U,TOL,PRINTW)
X0 = inistate(A,B,C,Y,U);
X0 = inistate(A,C,Y);
[x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW)
:SYS given system, syslin(dt,A,B,C,D) : :Y the output of the system : :U the input of the system : :TOL TOL is the tolerance used for estimating the rank of matrices.
If TOL > 0, then the given value of TOL is used as a lower bound for the reciprocal condition number. Default: prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision.
| = 1: | print warning messages; |
|---|
: := 0: do not print warning messages. :
Default: PRINTW = 0. : :X0 the estimated initial state vector : :V orthogonal matrix which reduces the system state matrix A to a
real Schur form
:
inistate Estimates the initial state of a discrete-time system, given the (estimated) system matrices, and a set of input/output data.
X0 = inistate(SYS,Y,U,TOL,PRINTW) estimates the initial state X0 of the discrete-time system SYS = (A,B,C,D), using the output data Y and the input data U. The model structure is :
x(k+1) = Ax(k) + Bu(k), k >= 1,
y(k) = Cx(k) + Du(k),
The vectors y(k) and u(k) are transposes of the k-th rows of Y and U, respectively.
Instead of the first input parameter SYS (an syslin object), equivalent information may be specified using matrix parameters, for instance, X0 = inistate(A,B,C,Y,U); or X0 = inistate(A,C,Y);
[x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) returns, besides x0, the orthogonal matrix V which reduces the system state matrix A to a real Schur form, as well as an estimate of the reciprocal condition number of the coefficient matrix of the least squares problem solved.