A unifying approach of LTI discrete-time state observers by means of complementary matrices

This paper deals with the generalization of state observers in the framework of LTI deterministic discrete-time systems using complementary matrix formalism. Four necessary and sufficient general conditions have been established in the design of any type of state observer. Furthermore, necessary sufficient intrinsic conditions have been deduced. Respecting these intrinsic conditions guarantees satisfaction of the preceding general conditions. An illustrative example is also included.