H_infinity controller synthesis with time-domain constraints

V. Balakrishnan

IEEE Trans. Aut. Control, AC-42(8):1179-1186, August 1997

Abstract: For a class of discrete-time linear time-invariant (LTI) plants, we present necessary and sufficient conditions for the existence of a discrete-time LTI controller that ensures that the H^infinity norm of a closed-loop map of interest is less than a prespecified level, subject to time-domain constraints on this closed-loop map. In cases when such an LTI controller does not exist, we show that the problem of finding an LTI controller that satisfies the input-output constraints with the smallest error can be posed as a convex optimization problem based on linear matrix inequalities. We also consider briefly other related problems that can be solved completely using a similar approach, namely controller synthesis to minimize the optimally scaled H^infinity norm, and controller synthesis to maximize the guaranteed dissipation.

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