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The paper applies the difference equations to unify the study of observability and controllability conditions of discrete-time multi-input multi-output (MIMO) nonlinear control systems. The necessary and sufficient condition for irreducibility of the set of nonlinear multi input- multi output (MIMO) is presented in terms of the greatest common left divisor of two polynomial matrices describing the behavior of the system which is suitable for constructing an observable and accessible state space realization. We show that the concepts of controllability and observability are related to systems of difference equations. It is well known that a solvable system of linear algebraic equations has a solution if and only if the rank of the system matrix is full .This method is more clear, straight-forward and therefore better suited for implementation in different computer packages such as Matlab.

Observability and Controllability of MIMO Control Systems via Difference Equations