Generalized Dissipativity-Based Receding Horizon FIR Filtering with Deadbeat Property

This paper proposes a new approach to designing the receding horizon finite impulse response (FIR) filter based on the generalized dissipativity concept. A new sufficient condition is established in the form of the linear matrix inequality (LMI) and linear matrix equality (LME) for generalized dissipative FIR filtering with deadbeat property. In contrast to the existing works on FIR filtering, this paper presents the $H_{\infty}$ FIR filter, the $l_{2}-l_{\infty}$ FIR filter, the passive FIR filter, and the $(\cal{Q}, \cal{S}, \cal{R})-\alpha$ -dissipative FIR filter in a unified framework. A design condition for the generalized dissipative FIR filter (GDFF) without LME is also discussed. By means of a numerical example, it is shown that the developed approach provides an FIR filter with more robustness against unpredictable short-time model changes than the existing ones.