Bezout factors and L1-optimal controllers for delay systems using a two-parameter compensator scheme

The authors consider 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 (1992) in the L²-setting. Optimal tracking involves the resolution of L¹-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 ℬˆ(0). Finally, they solve several general L¹-optimization problems and give an algorithm to solve the optimal robust control problem for a large class of delay systems