ROBUST TRACKING OF LINEAR MIMO TIME-VARYING SYSTEMS

The asymptotic properties of the linear multivariable time-varying tracking systems, constructed from the fixed-degree matrix polynomials, under the unmodeled dynamics and external disturbances are investigated in this paper. The robust controllers are designed based on the frozen-time approach. First, the robust stabilization is assured. The asymptotic robust stability conditions on both the mismodeling errors, which only depend on the frozen-time computations, and the variation rates of the perturbed plants are found and quantitatively characterized. And, more essentially, the robust tracking performance is achieved. It is shown that if the time-varying plants and the time-varying nominal models are asymptotically slowly varying, then the exact tracking requirement, which has zero steady reference command signals tracking errors, is achieved in the time-varying feedback systems under the situations of the unmodeled dynamics, external disturbances and time-varying effects of the systems. The corresponding permissible ranges of mismodeling errors and the robustness enhancement are provided and discussed.