Continuous-Time Deadbeat $H_{2}$ FIR Filter

This brief proposes a new continuous-time state-space H₂ finite impulse response (FIR) filter with the embedded deadbeat property for linear systems undergoing external disturbances. The new filter is called the continuous-time deadbeat H₂ FIR filter (CTDH2FF). The proposed filter demonstrates H₂ performance under disturbances and the deadbeat property otherwise. The CTDH2FF can be implemented by solving two matrix differential equations for given boundary conditions. A new formula for the minimum H₂ norm of the CTDH2FF is also discussed. Numerical simulations show that the proposed filter has much better robustness against unexpected short-term model changes than the existing filters.