Robust State-Feedback Controller Design for Fuzzy Descriptor Markovian Jump Systems Based on An LMI Approach

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of uncertain nonlinear descriptor Markovian jump systems described by a TakagiSugeno (TS) fuzzy model with Markovian jumps. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor Markovian jump 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 descriptor systems. A numerical example is provided to illustrate the design developed in this paper.