For the descriptor system Ex = Ax + Bu, y = Cx + Du, an observer of th
e order p = rank E - p1 (0 less-than-or-equal-to p1 less-than-or-equal
-to rank E) is developed. It is not assumed that the descriptor system
s are necessarily regular. The derivation is straightforward using onl
y an algebraic approach. The existence conditions of the observer are
also presented. These conditions are less restrictive than existing on
es. Some illustrative examples are included.