On standard H∞ control of processes with a single delay

This note presents a frequency domain method to solve the standard control problem for processes with a single delay. For a given bound on the closed-loop norm, there exist proper stabilizing controllers that achieve this bound if and only if both the corresponding delay-free problem and an extended Nehari problem with a delay (or a one-block problem) are all solvable. The solvability of the extended Nehari problem (or the one-block problem) is equivalent to the nonsingularity of a delay-dependent matrix. The solvability conditions of the standard control problem with a delay are formulated in terms of the existence of solutions to two delay-independent algebraic Riccati equations and a delay-dependent nonsingularity property. All suboptimal controllers solving the three problems are, respectively, parameterized as a structure incorporating a modified Smith predictor.