Robust H∞ State-Feedback Control Design for Fuzzy Singularly Perturbed Systems with Markovian Jumps: An LMI Approach 175 Robust H∞ State-Feedback Control Design for Fuzzy Singularly Perturbed Systems with Markovian Jumps: An LMI Approach

This paper examines the problem of designing a robust H∞ state-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. 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. A numerical example is provided to illustrate the design developed in this paper.