Deadbeat Dissipative FIR Filtering

In this paper, we propose a new deadbeat dissipative filter with a finite impulse response (FIR) structure for linear discrete-time systems with external disturbance; this filter is called a deadbeat dissipative FIR filter (DDFF). The new filter ensures (Q, S, R)-α-dissipativity and the deadbeat property based on three slack matrix variables. By tuning the weighting parameters provided by the (Q, S, R)-α-dissipativity in the proposed DDFF, we present H
_∞
and passive FIR filters in a unified framework and investigate ways of improving the ℓ
₂
stability, bounded- disturbance bounded-error stability, and robustness of FIR filters. The gain matrix of the proposed DDFF is obtained by solving a convex problem using the linear matrix inequality approach. Two numerical examples are provided to demonstrate the effectiveness and advantages of the obtained theoretical results.