Decoupling
Numerical aspects of linear control

MIMO systems are difficult to control directly by trial and error, as a change in a single input can affect many, if not all, outputs. It would be much simpler if each input (or block of inputs) influenced only one output (or block of outputs). Separating a system into independent subsystems is called decoupling. There are several types of decoupling, depending on the form of the transfer function.

Let's consider, for a square system with the same number of inputs and outputs (p = m), the case of diagonal decoupling, which consists in making the matrix G diagonal. In this case, output i will only be influenced by input i. If G is singular, the system's outputs are not linearly independent. If G is singular, the system's outputs are not linearly independent and it will be impossible to make it diagonally decoupled, whatever the form of control.

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