Abstract
Linear discrete- and continuous-time systems with multiplicative noise and polytopic-type parameter uncertainties are considered. The problems of \(H_\infty \) state-feedback control and filtering of these systems are addressed. These problems are solved by applying a vertex-dependent Lyapunov function, based on the Finsler’s lemma, which considerably reduces the overdesign associated with the classical “quadratic” design that applies a single Lyapunov function for the whole parameters range. In both settings, a cost function is defined which is the expected value of the standard \(H_\infty \) performance index with respect to the stochastic multiplicative parameters. The results are demonstrated via two numerical examples.
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Gershon, E., Shaked, U. (2019). Robust Vertex-Dependent Control and Filtering of Stochastic Systems. In: Advances in H∞ Control Theory. Lecture Notes in Control and Information Sciences, vol 481. Springer, Cham. https://doi.org/10.1007/978-3-030-16008-1_10
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DOI: https://doi.org/10.1007/978-3-030-16008-1_10
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