On the dead-time compensation from L1 perspectives

It is known that both H 2 and H optimization problems for dead-time systems are solved by controllers having the so-called modified Smith predictor (dead-time compensator) structure. This note shows that this is also true for the L1 control problem. More precisely, it is demonstrated that the use of the modified Smith predictor enables one to reduce the standard L1 problem for systems with a single loop delay to an equivalent delay-free problem. The (sub)optimal solution therefore always contains the modified Smith predictor.