On the dead-time compensation from L1 perspectives

It is known that both H² 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.