H∞ control for two-dimensional Markovian jump systems with state-delays and defective mode information
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OriginalversjonWei, Y., Wang, M., Karimi, H. R., & Qiu, J. (2013). H∞ control for two-dimensional Markovian jump systems with state-delays and defective mode information. Mathematical Problems in Engineering, 2013. doi: 10.1155/2013/520503 10.1155/2013/520503
This paper investigates the problem of H∞ state-feedback control for a class of two-dimensional (2D) discrete-time Markovian jump linear time-delay systems with defective mode information. The mathematical model of the 2D system is established based on the well-known Fornasini-Marchesini local state-space model, and the defective mode information simultaneously consists of the exactly known, partially unknown, and uncertain transition probabilities. By carefully analyzing the features of the transition probability matrices, together with the convexification of uncertain domains, a new H∞ performance analysis criterion for the underlying system is firstly derived, and then the H∞ state-feedback controller synthesis is developed via a linearisation technique. It is shown that the controller gains can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to verify the effectiveness of the proposed design method.
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/520503 Open Access