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

This paper investigates the problem of designing a robust output 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, LMIbascd 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.