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.

### See Also

`findBD` `findx0BD`