Regional nonlinear H^∞ filtering

The structure of the nonlinear H^∞ filter in the neighborhood of the estimated trajectory is investigated and a bound on the size of the neighborhood that allows this structure is determined, both for finite and infinite horizons. Riccati inequalities that depend on the estimated trajectory are derived for finding the filter gain matrix and an algorithm for calculating the bound on the size of the above neighborhood is presented. Explicit formulas are obtained in the infinite horizon case for the minimum achievable disturbance attenuation level, the size of the neighborhood, and the corresponding filter gain.