In this chapter, the mixed H2/H∞ filtering problem is investigated for systems with deterministic uncertainties and stochastic nonlinearities, where the nonlinearities are characterized by statistical means. It is the aim to design a filter such that, for all admissible stochastic nonlinearities and deterministic uncertainties, the overall filtering process is exponentially mean‐square quadratically stable, the H2 filtering performance is achieved, and the prescribed disturbance attenuation level is guaranteed in an H∞ sense. New formulas are derived for exponentially mean‐square quadratic stability, H2 performance and H∞ performance. In particular, due to the introduction of the stochastic nonlinearities, a new lemma about the relations between the stability of the system and the non‐negative definite solution to matrix inequality is developed for deriving H2 performance, which is actually the extension of results for linear systems. The solution to the H2/H∞ filtering problem is enforced within a unified linear matrix inequality framework.
Robust Mixed H2/H∞ Filtering
2015-03-16
24 pages
Article/Chapter (Book)
Electronic Resource
English
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