On the generalization of state feedback decoupling theory

The theory of state-variable feedback decoupling in multivariable control systems is generalized to include the case where a subset of the output set is the candidate for decoupling. Systems in which such decoupling is employed will be termed "partially decoupled." Decoupling a selected set of outputs, when achieved by using a state feedback matrix and a nousingular ( ) input matrix , will be called -input decoupling (MID), to reflect the restriction on the input matrix. An algorithm, developed by Silverman for constructing inverse systems, is shown to play an essential role in the MID problem, and using matrices constructed in the algorithm, necessary, and sufficient conditions for -input decoupling the specified set of outputs are obtained. As would be expected, these necessary and sufficient conditions include the existing conditions for decoupling all system outputs as a special case. An example is given illustrating the results.