Decoupling linear multiinput multioutput plants by dynamic output feedback: An algebraic theory

This paper presents an algebraic theory for the design of a decoupling compensator for linear time-invariant multiinput multioutput systems. The design method uses a two-input one-output compensator, which gives a convenient parametrization of all diagonal input-output (I/ O) maps and all disturbance-to-output (D/O) maps achievable by a stabilizing compensator for a given plant. It is shown that this method has two degrees of freedom: any achievable diagonal I/O map and any achievable D/O map can be realized simultaneously by a choice of an appropriate compensator. The difference between all achievable diagonal and nondiagonal I/O maps and the "cost" of decoupling is discussed for some particular algebraic settings.