Abstract
In this article, we introduce, formulate and solve the W-1,W-2 and W-1,W-infinity estimation problems. We propose proportional, proportional-derivative and proportional-integral ( PI) filters for each problem, and we derive sufficient conditions for the existence of optimal filter gains in terms of new Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations. The output-feedback W-1,W-2 and W-1,W-infinity control problems are also re-solved using the separation principle. We show that, by combining an optimal estimator with state-feedback control, a viable optimal output-feedback controller can be synthesised.