L2–L∞ control of nonlinear fuzzy Itô stochastic delay systems via dynamic output feedback

This paper addresses the L2–L∞ dynamic output feedback (DOF) control problem for a class of nonlinear fuzzy Itô stochastic systems with time-varying delay. The focus is placed upon the design of a fuzzy DOF controller guaranteeing a prescribed noise attenuation level in an L2–L∞ sense. By using the slack matrix approach, a delay-dependent sufficient condition is derived to assure the mean-square asymptotic stability with an L2–L∞ performance for the closed-loop system. The corresponding solvability condition for a desired L2–L∞ DOF controller is established. Since these obtained conditions are not all expressed in terms of linear matrix inequality (LMI), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be easily solved numerically. Finally, numerical results are presented to emonstrate the usefulness of the proposed theory.