Abstract
Until now, H∞ control theory has been aided by small gain or norm-bounding techniques to supply robust stability conditions. Many practical applications of robust feedback control involve constant real parameter uncertainty, whereas small gain or norm-bounding techniques guarantee robust stability against complex, frequency-dependent uncertainty, thus entailing undue conservatism and unnecessarily sacrificing performance. In thiss paper, we consider the robust stability by the Hurwitz criterion which is sufficient and necessary, and robust performance by satisfying an H∞ sensitivity constraint for an SISO minimum phase plant having parametric perturbation. We design the compensator so that the complementary sensitivity function is a low-pass filter function for an assumed nominal plant which does not necessarily exist in the family of real models. Thus the compensator robustly stabilizes the closed-loop system for a plant with large parametric variation. Furthermore, we obtain satisfactory performance in the low-frequency domain. Robust stability criteria, robust performance criteria and a number of assumptions are imposed. The satisfaction of these assumptions guarantees the existence of a proper compensator which satisfies mixed criteria.
