H∞Enhanced Control Design of Discrete-Time Takagi-Sugeno State-Multiplicative Noisy Systems

Design conditions for existence of the H∞ state feedback control for Takagi-Sugeno fuzzy discrete-time stochastic systems with state-multiplicative noise, stabilizing the closed-loop in such way that the quadratic performance in the mean is satisfied, are presented in the paper. Using newly introduced enhanced form of the bounded real lemma for such stochastic systems, the LMI-based procedure is provided for computation of gain matrices of the state control law, realized in the parallel distributed compensation structure. The approach is illustrated on an example, demonstrating the validity of the proposed method