Dissipativity-Based Sampled-Data Reliable Control Design for T-S Fuzzy System Using Limited Bessel-Legendre Inequality

This paper investigates the dissipativity-based reliable control for Takagi–Sugeno (T-S) fuzzy systems under time-varying sampling intervals based on the input delay approach. By constructing a novel Lyapunov–Krasovskii functional and using a limited Bessel–Legendre inequality that makes full use of the available information on the variable sampling pattern, a sufficient stabilization criterion is obtained to guarantee the sampled-data systems to be asymptotically stable and strictly
$(\mathcal {Q},\mathcal {S},\mathcal {R})$
-
$\gamma $
-dissipative. Based on the criterion, a desired dissipativity-based sampled-data reliable controller is proposed. Moreover, in the case of no the actuator failure and
$\gamma $
-dissipative, some new stability and stabilization criteria are also obtained. It is shown that the new stability and stabilization criteria can provide a larger upper bound of the sampling interval than some existing works. The effectiveness and superiority of the design methods developed in this paper are demonstrated by two simulation examples.