2007
DOI: 10.1109/tfuzz.2006.889841
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Fuzzy $H_\infty$ Filter Design for a Class of Nonlinear Discrete-Time Systems With Multiple Time Delays

Abstract: This paper studies the fuzzy filter design problem for signal estimation of nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. First, the Takagi-Sugeno (T-S) fuzzy model is used to represent the state-space model of nonlinear discrete-time systems with time delays. Next, we design a stable fuzzy filter based on the T-S fuzzy model, which guarantees asymptotic stability and a prescribed index for the filtering error system, irrespective of the time delays and uncertain d… Show more

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Cited by 132 publications
(55 citation statements)
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“…It is noted that the common Lyapunov function proposed in [40] is not applicable to the distributed H ∞ filtering design for this case in this example. However, by applying Theorem 1, the feasible solutions of γ min = 3.9555 for the full-order filter and γ min = 6.5599 for the reduced-order filter are obtained, and the corresponding filter gains are Example 2.…”
Section: Examplementioning
confidence: 97%
See 1 more Smart Citation
“…It is noted that the common Lyapunov function proposed in [40] is not applicable to the distributed H ∞ filtering design for this case in this example. However, by applying Theorem 1, the feasible solutions of γ min = 3.9555 for the full-order filter and γ min = 6.5599 for the reduced-order filter are obtained, and the corresponding filter gains are Example 2.…”
Section: Examplementioning
confidence: 97%
“…The region index set is J i = {1, 2, 3}. Now, considering the case of full-order filter with a i = 0.9, the common Lyapunov function proposed in [40] is not applicable to the distributed H ∞ filtering design for this case in this example. However, by applying Theorem 1, the H ∞ filtering performance γ min = 3.3755 is obtained, and the obtained filter gains are Given the initial conditions x 1 (0) =[ 1.3, 0] T , x 2 (0) = [ 1.1, 0] T , and assume that the external disturbances satisfy w 1 (t) = 5e −0.02t sin(t) and w 2 (t) = 5e −0.02t cos(t), it is easy to see from Figs.…”
Section: Examplementioning
confidence: 99%
“…For example, the fuzzy ∞ filtering has been discussed in [50] for a class of nonlinear discrete-time systems with both multiple time-delays and unknown bounded disturbances. For the same kind of time-delays, in [51], a full-order ∞ filter has been designed to guarantee that the filtering error dynamics are stochastically stable and the given ∞ attenuation level is guaranteed.…”
Section: T-s Fuzzy Control and Filtering With Communicationmentioning
confidence: 99%
“…Among different fuzzy models, the well-known Takagi-Sugeno (T-S) fuzzy model has attracted considerable research attention [1][2][3][4][5] and a large amount of literature has appeared on the fundamental issues of stability and stabilization for T-S fuzzy systems (see, e.g., [6,7] and the cited therein). Very recently, Choi et al [8] put forward a new method to formulate a framework that can describe T-S fuzzy systems with time-varying input delay and output constraints based on ( , , ) − -dissipativity, which not only synthesized ∞ control and passivity control, but also applied the obtained results to different road conditions.…”
Section: Introductionmentioning
confidence: 99%