8 Discrete-time Systems: General Filtering

Abstract

In Chapter 7 we introduced the solution to the output-feedback control problem for the time-varying, discrete-time systems with state-multiplicative noise, for both the finite and the infinite time cases [43],[39]. This solution is based on solving the filtering part using a Luenberger-type observer and applying the stochastic BRL. In this chapter, similarly to Chapter 3, we apply a general type filter for the solution of both: the H∞ and the mixed H₂/H∞ stationary filtering cases. We also allow for a deterministic polytopic-type uncertainties in the system matrices.