Robust H State-Feedback Control for Uncertain Fuzzy Markovian Jump Systems: LMI-Based Design

This paper investigates the problem of designing a robust state-feedback controller for a class of uncertain Markovian jump nonlinear systems that guarantees the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value. First, we approximate this class of uncertain Markovian jump nonlinear systems by a class of uncertain Takagi-Sugeno fuzzy models with Markovian jumps. Then, based on an LMI approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear systems to have an H∞ performance are derived. An illustrative example is used to illustrate the effectiveness of the proposed design techniques. Keywords— Robust H∞; Fuzzy Control; Markovian Jump Systems; LMI