Robust H∞ Filtering

In control engineering research, the robust filtering (state estimation) problem arises out of the desire to determine estimates of unmeasurable state variables for dynamical systems with uncertain parameters. Along this way, the robust filtering problem can be viewed as an extension of the celebrated Kalman filter [3,4] to uncertain dynamical systems. The past decade has witnessed major developments in robust and H_∞ – control theory [1,2,5-8] with some focus on the robust filtering problem using different approaches. In [10-18], a linear H_∞ – filter is designed such that the H_∞–norm of the system, which reflects the worst case gain of the transfer function from the disturbance inputs to the estimation error output, is minimized. On the other hand, by constructing a state estimator which bounds the mean square estimation error [12], one can develop a robust Kalman filter. Indeed, the H_∞ – filtering is superior to the standard H₂ – filtering since no statistical assumption on the input is needed. It considers essentially the exogenous input signal to be energy bounded rather than Gaussian.