This paper deals with the generalization of state observers in the framewor
k of LTI deterministic discrete-time systems using complementary matrix for
malism. Four necessary and sufficient general conditions have bren establis
hed in the design of any type of state observer. Furthermore, necessary suf
ficient intrinsic conditions have been deduced. Respecting these intrinsic
conditions guarantees satisfaction of the preceding general conditions. An
illustrative example is also included.