KETEROBSERVASIAN SISTEM LINIER DISKRIT

Abstract

Given the following discrete time-invariant linear control systems:
where x 2 R
n
x(t + 1) = Ax(t) + Bu(t);
y(t) = Cx(t);
is the state vector, u 2 R
m
is an input vector, y 2 R
r
is dened as an
output, A 2 R
nn
, B 2 R
nm
, and t 2 Z
is dened as time. Linear system is said to be
observable on the nite time interval [t
0
; t
+
f
] if any initial state x
is uniquely determined
by the output y(t) over the same time interval. In order to examine the observability
of the system, we will use a criteria, that is by determining the observability Gramian
matrix of the system is nonsingular and rank of the observability matrix for the system
is n.