An L∞ optimal performance approach to robust feedback control

This paper proposes a design technique to minimize a weighted L_∞ performance measure over all disturbances in a given set. This disturbance set is also characterized by a weighted L_∞ norm. The technique can accommodate hard constraints on regulated and manipulated variables. The main result is that each closed-loop mapping must lie in the `polar´ defined by the disturbance set. The model reference transformation parameter Q is subsequently computed as a finite impulse response filter. The resulting closed-loop system will reject persistent bounded disturbance inputs. A novel method of computation is also outlined which formulates the optimal design problem as a reasonably-sized linear program.