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This paper examines the problem of designing a robust H∞ state-feedback and output feedback controller for a class of uncertain Markovian jump nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model with Markovian jumps. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear singularly perturbed systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear singularly perturbed systems.
Decision and Control, 2004. CDC. 43rd IEEE Conference on (Volume:1 )
Date of Conference: 17-17 Dec. 2004