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This paper is about theandfiltering of Markov Jump Systems subject to a class of nonlinearities which include them on the Lur'e systems framework. The proposed filters are robust to nonlinearities belonging to a given sector with maximum slope. With regard to the availability of the Markov parameter, we present strategies which allow us to design either mode-dependent and modeindependent filters, with sector bound optimisation. The results are illustrated by two examples.

ℋ 2 and ℋ ∞ Filtering for Continuous-Time Markov Jump Lur'e Systems with Sector Bound Optimization