H∞ Filtering of Discrete-Time Systems
This chapter focuses on the H∞ filtering of discrete-time systems. The Riccati equation approach is first applied to derive H∞ a priori and a posteriori filters in both the finite horizon and stationary cases. The chapter presents a polynomial approach to the H∞ filtering problem whose solution relies on J-spectral factorization. An application of H∞ filtering to channel equalization is given to illustrate the design of an H∞ filter. The chapter also presents several versions of bounded real lemma which play a crucial role in deriving an H∞ filter. It explores the stationary H∞ estimation using a polynomial approach. The chapter shows that a polynomial approach is often preferred in signal processing and communications due to its efficient computation. It considers a linear time-invariant channel model described by an nth order finite impulse response filter.