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This paper investigates the roundoff noise effect in the digital controller on the closed-loop output for a discrete-time feedback control system. Based on a polynomial parametrization approach, a sparse controller structure is derived. The performance of the proposed structure is analyzed by deriving the corresponding expression of closed-loop roundoff noise gain and the problem of finding optimized sparse structures is solved. A numerical example is presented to illustrate the design procedure and the performance of the proposed structure compared with those of some existing well-known structures.

OPTIMAL SPARSE CONTROLLER STRUCTURE WITH MINIMUM ROUNDOFF NOISE GAIN