Robust ℋ ∞ control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach

Examination is made of the problems of designing robust ℋ∞ state-feedback and output feedback controllers for a class of uncertain Markovian jump nonlinear singularly perturbed systems described by a Takagi–Sugeno fuzzy model with Markovian jumps. Based on the 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 problems are given in terms of linear matrix inequalities that are independent of the singular perturbation ɛ, when ɛ 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. A numerical example is provided to illustrate the design developed in this paper.