In this paper, the problem of l 2 - l ∞ filtering for a class of discrete-time Takagi-Sugeno (T-S) fuzzy time-varying delay systems is studied. Our attention is focused on the design of full- and reduced-order filters that guarantee the filtering error system to be asymptotically stable with a prescribed H ∞ performance. Sufficient conditions for the obtained filtering error system are proposed by applying an input-output approach and a two-term approximation method, which is employed to approximate the time-varying delay. The corresponding full- and reduced-order filter design is cast into a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, simulation examples are provided to illustrate the effectiveness of the proposed approaches.

This paper is concerned with the problems of dissipativity analysis and synthesis for discrete-time Takagi-Sugeno fuzzy systems with stochastic perturbation and time-varying delay. First, a novel model transformation method is introduced to pull the time-varying delay uncertainty out of the original system. Consequently, the transformed model is composed of a linear time-invariant system and a norm-bounded uncertain subsystem. By using this model transformation method combined with the Lyapunov-Krasovskii technique, sufficient conditions of the dissipativity are established. Then, a fuzzy controller is designed to guarantee the dissipative performance of the closed-loop system. Finally, three examples are presented: one shows the effectiveness of model transformation method, the second performs the comparison with alternative approaches, and the third illustrates the applicability of the proposed dissipative control methods.

This paper is concerned with the problem of H ∞ model approximation for discrete-time Takagi-Sugeno (T-S) fuzzy time-delay systems. For a given stable T- S fuzzy system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in an H ∞ performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic stability with an H ∞ error performance for the error system. Then, the H ∞ model approximation problem is solved by using the projection approach, which casts the model approximation into a sequential minimization problem subject to linear matrix inequality (LMI) constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, H ∞ model approximation with special structures is obtained, i.e., delay-free model and zero-order model. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

The paper deals with the robust fault detection problem for Takagi-Sugeno (T-S) fuzzy Ito stochastic systems. Our aim is to develop a robust fault detection approach to the T-S fuzzy systems with Brownian motion. By using a general observer-based fault detection filter as a residual generator, the robust fault detection is formulated as a filtering problem. Attention is focused on the design of both the fuzzy-rule-independent and the fuzzy-rule-dependent fault detection filters guaranteeing a prescribed noise attenuation level in an H infin sense. Sufficient conditions are proposed to guarantee the mean-square asymptotic stability with an H infin performance for the fault detection system. The corresponding solvability conditions for the desired fuzzy-rule-independent and fuzzy-rule-dependent fault detection filters are also established. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

In this note, the fault detection filtering problem is solved for nonlinear switched stochastic system in the T-S fuzzy framework. Our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with Brownian motion. Based on observer-based fault detection fuzzy filter as a residual generator, the proposed fault detection is formulated as a fuzzy filtering problem. By the utilization of the average dwell time technique and the piecewise Lyapunov function technique, the fuzzy-parameter-dependent fault detection filters are designed that guarantee the resulted error system to be mean-square exponential stable with a weighted H ∞ error performance. Then, the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique. Finally, simulation has been presented to show the effectiveness of the proposed fault detection technique.