Abstract
We solve a robust receding horizon finite impulse response (FIR) filtering problem in a discrete-time state space in three frequency regions under severe disturbances. Novel design conditions are derived for the finite frequency region FIR filter, called FFFF or 4F, in terms of the linear matrix inequality and equality constraint, such that the 4F ensures the $H_{\infty }$ performance and deadbeat property. The 4F attenuates the effects of disturbances in the user-given low-, middle-, and high-frequency regions. The new design conditions, which do not involve the equality constraint, are also investigated. An example of applications for the $F$ -404 turbofan engine system demonstrates the much better performance of the proposed 4F compared with the existing entire frequency FIR filter and the finite frequency region infinite impulse response filter.
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