A new solution to the inducedl∞finite impulse response filtering problem based on two matrix inequalities

In this paper, we use an induced l∞ approach to create a new filter with a finite impulse response (FIR) structure for state-space models with external disturbances. This filter is called an induced l∞ FIR filter (ILIFF). The proposed ILIFF’s gain matrix can be determined by solving a linear matrix inequality problem for a fixed positive scalar variable. An illustrative example is given to demonstrate the effectiveness of the ILIFF.