EFFICIENT EIGENVALUE ASSIGNMENTS FOR GENERAL LINEAR MIMO SYSTEMS

This paper deals with the transformation of linear, multi-input multi-output (MIMO) systems into Frobenius canonical form, with the ultimate objective of developing a new, computationally efficient methodology for a pole placement procedure. Both time-invariant and time-varying systems are considered. The conventional pole placement steps for time-invariant SISO (single-input single-output) systems are generalized for both classes. This is a unique study of the expansion of the pole placement capability, in particular for time-varying MIMO systems. This depth of generalization has been neglected in the past due to its complex formulation. The practical advantage of the proposed technique is that it does not require the coefficients of the characteristic polynomial, the eigenvalues of the original system, or the coefficients of the characteristic polynomial of the transformed system. The repercussions of such a development are expected in nonlinear systems theory as well considering the fact that some recently developed techniques yield exact I/O linearization with time-varying coefficients.