Solution of the H∞ optimal linear filtering problem for discrete-time systems

The solution of l₂ (minimum variance) and H_∞ estimation problems is considered using a polynomial systems approach. The results for the l₂ filtering problem, which corresponds with Wiener or Kalman filtering/prediction, are first presented in polynomial matrix form. Attention then turns to the solution of the H_∞ estimation problem for scalar systems. Numerous examples are presented to illustrate the computational procedures. The two types of estimator are appropriate to very different estimation problems and the new H _∞ devices should be valuable in certain application areas