Bezout factors and L-1-optimal controllers for delay systems using a two-parameter compensator scheme

The authors consider in this paper the simultaneous problem of optimal robust stabilization and optimal tracking for single-input/single-output (SISO) systems in an L-∞-setting using a two-parameter compensator scheme. Optimal robustness is linked to the work done by Georgiou and Smith in the L-2-setting. Optimal tracking involves the resolution of L-1-optimization problems. The authors consider in particular the robust control of delay systems. They determine explicit expressions of the Bezout factors for general delay systems which are in the Callier-Desoer class β(0). Finally, they solve several general L-1-optimization problems and give an algorithm to solve the optimal robust control problem for a large class of delay systems.