Observer-basedH∞-control for discrete-time T–S fuzzy systems

This article further studies the observer-based H ∞-control problem for discrete-time Takagi–Sugeno (T–S) fuzzy systems. By using fuzzy Lyapunov functions and introducing slack variables, a sufficient condition, which can guarantee observer-based H ∞-control performance for T–S fuzzy systems, is proposed in terms of a set of bilinear matrix inequalities. Moreover, in the so-called two-step procedure, results of the first step are allowed to select in order to reduce the conservatism of previous approaches. In comparison with the existing literature, the proposed approach not only provides more relaxed H ∞-control conditions but also ensures better H ∞-control performance. Finally, the validity and applicability of the proposed approach are successfully demonstrated through two numerical examples.