chapter  7
34 Pages

Ή∞ Filtering of Continuous-Time Systems

WithFrank L. Lewis, Lihua Xie, Dan Popa

This chapter deals with the design of estimators with an H∞ performance measure and where the only uncertainty in the system model is in the form of bounded energy noise signals, i.e., there is no uncertainty in the matrices of the system state-space model. In the H∞ filtering, the noise inputs are deterministic signals and are required to be energy-bounded. The chapter considers both the finite-horizon and stationary H∞ estimation problems. For the finite-horizon filtering, two situations are considered for the system initial state: one corresponds to the case when the initial state is unknown and the other the initial state is assumed to be zero. It discusses the Riccati equation approach and linear matrix inequality approach to the stationary H∞ filter design. Signal estimation setting is quite general and encompasses a number of typical situations that arise in the areas of control engineering and signal processing.