Optimal robust multi-purpose general feedback systems

Abstract

This paper studies the solution of the robust asymptotic tracking/disturbance rejection problem with minimum sensitivity for general feedback multivariable systems, namely, those in which the plant is two-input two-output and the compensator is two-input one output and there are exogenous signals in the two junctions between plant and compensator. The exogenous signals into the plant and junctions are asymptotically rejected, while the exogenous signal into the compensator is asymptotically tracked by one of the plant's output. Resides, the system is stable and the sensitivities are minimized, taking advantage of the two degrees of freedom provided by the compensator. The problem is solved for plant and compensator whose transfer function matrices are rational, using the factorization approach with the transfer function matrices factorized over proper and stable rational matrices. The paper is a development of results obtained in the solution of the asymptotic tracking/disturbance rejection problem with stability [3].