Measurable signal decoupling through self-bounded controlled invariants: minimal unassignable dynamics of feedforward units for pre-stabilized systems

A dynamic feedforward scheme enables measurable signal decoupling to be solved independently of other problems simultaneously present in the design of an actual control system, like e.g. plant pre-stabilization, robustness with respect to uncertainties, insensitivity to unaccessible disturbances, etc. The synthesis procedure, based on the properties of self-bounded controlled invariant subspaces, ensures the minimal complexity of the dynamic feedforward unit, in terms of the minimal unassignable dynamics, in the case of left-invertible systems and, on certain conditions, also in the case of non-left-invertible systems. The dynamic output feedback in charge of pre-stabilization, or, more generally, ensuring some robustness or insensitivity properties, does not affect the complexity of the dynamic feedforward unit. In fact, the particular layout where the feedback unit receives an input directly from the precompensator, preserves the set of the internal unassignable eigenvalues of the minimal self-bounded controlled invariant. Hence, it maintains the unassignable dynamics of the precompensator.