Scilab Function

inistate - Estimates the initial state of a discrete-time system

### Calling Sequence

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)

### Parameters

• 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.

• PRINTW : PRINTW is a switch for printing the warning messages.
• = 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
• rcnd : estimate of the reciprocal condition number of the coefficient matrix of the least squares problem solved.

### Description

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.