Approximate decoupling of multivariable control systems by linear state variable feedback

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Abstract
Linear time invariant multivariable systems whose parameters do not satisfy the necessary and sufficient conditions for complete decoupling aro considered. Systems aro considered whoso parameters are such that the decoupling matrix is singular. It is shown that it is still possible to approximately decouplo the system in the sense that r of the system's m scalar input-output pairs are completely decoupled, while the remaining m — r scalar input-output pairs remain coupled. It is further shown that the degree of decoupling possiblo depends on the rank of the decoupling matrix. A lemma is stated and proved that shows the existence of a decoupling scheme that decouples tho system to the extent that the output, yi, is dependent on at most the input m;(. if i≤r.

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