IEEE Transactions on Automatic Control, Vol.48, No.6, 1097-1103, 2003
On standard H-infinity control of processes with a single delay
This note presents a frequency domain method to solve, the standard H-infinity control problem for processes with a single delay. For a given bound on the closed-loop H-infinity norm; there exist proper stabilizing controllers that achieve this bound if and only if both the corresponding delay-free H-infinity 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 H-infinity 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.