Decoupling in the Design and Synthesis of Multivariable Control Systems

Absfracf-Necessary and sdicient conditions far the "decou- pling" of an m-input, m-output time-invariant linear system using state variable feedback are determined. Given a system which satis- fies these conditions, i.e., which can be decoupled by state variable feedback, the class of all feedback matrices which decouple the system is characterized. The characterization of @ is used to deter- mine the number of closed-loop poles which can be specified for the decoupled system and to develop a synthesis technique for the real- ization of desired closed-loop pole configurations. Transfer matrix consequences of decoupling are examined and practical implications discussed through numerical examples.