A NEW REPRESENTATION OF SISO SYSTEMS FOR STUDYING APPROXIMATED MODELS

A new type of nonlinear matrix is introduced. The existence of a particular solution of the above equation is proved. The solution considered contains information regarding both the closed-loop characteristic values and the signature. A new type of representation for SISO system and a new class of invariant quantities are proposed. The ease with which the transformation makes it possible to represent the original system in the new state coordinate is established by the diagonalization of a matrix with real eigenvalues. The diagonal transformation that allows passage from the closed balanced realization to the realization discussed here guarantees the equivalence between reduced models in the two representations. This fact represents an alternative way to obtain suitable reduced models for closed-loop purposes.