ABSTRACT
Kalman’s concept of the state controllability has become a fundamental control concept, [199]-[203]. E. G. Gilbert [66] generalized it to the MIMO systems. M. L. J. Hautus [186] established for them the simple form of the controllability criterion in the complex domain. J. E. Bertram and P. E. Sarachik [14] broadened the state controllability
concept to the output controllability concept. Both the state controllability concept and the output controllability concept
consider the system possibility of steering a state or an output from any initial state or from any initial output to another state or another output, in general, or to the zero state or to the zero output, in particular, respectively. R. W. Brockett and M. D. Mesarovi´c (Mesarovitch) [20] introduced the con-
cept of functional (output) reproducibility , called also the output function controllability [8, page 313], [29, page 216], [319, pages 72 and 164], in which the target is not a particular output (e.g., the zero output) but a given function representing a reference (desired) output response. This concept concerns the systems free of any external disturbance action. All these controllability concepts assume the nonexistence of any external
perturbations acting on the system. The only external in‡uences on the system are control actions. Dynamic systems, in general, and plants, hence their control systems, in par-
ticular, are subject in reality to actions of unpredictable external perturbations (called usually disturbances).
