Abstract
Filtering has been one of the important problems in the areas of control and signal processing, which is usually used to estimate unavailable variables of a given system through noisy measurement. Particularly, \(H_\infty \) filtering has become a hot topic due to the powerful signal estimation and good robustness performance. In this chapter, the problem of \(H_\infty \) filtering for SMJSs will be considered. When there are uncertainties in TRM, conditions for robust \(H_\infty \) filtering are presented for SMJSs in terms of LMIs. Based on a MD Lyapunov function approach, a PMD filter is designed and the developed conditions are expressed in LMIs. In contrast to the traditionally mode-dependent or mode-independent filtering method, the stochastic property of mode available to a filter is employed in the filter design. Finally, another general robust \(H_\infty \) filtering is considered, where the designed filter can tolerate uncertainties on its parameters, and the TRM satisfy general cases in terms of being uncertain and partially unknown. LMI-based conditions are developed, which is used to deal with a special case of mode-independent filtering.
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Wang, G., Zhang, Q., Yan, X. (2015). Filtering. In: Analysis and Design of Singular Markovian Jump Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-08723-8_6
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DOI: https://doi.org/10.1007/978-3-319-08723-8_6
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