## Name

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.