A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems
Citations
637 citations
406 citations
Cites background or result from "A New Approach to Stability Analysi..."
...It can be seen that the methods proposed in this paper are better than the recently published results in [12] and [33]....
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...which has been considered in [12] and [33]....
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...For different d ̄ d ̄ = 3 d ̄ = 5 d ̄ = 10 d ̄ = 12 Theorem 1 of [12] d̄ = 14 d̄ = 16 d̄ = 20 d̄ = 21 Theorem 3 of [33] d̄ = 23 (m = 3) d̄ = 25 (m = 5) d̄ = 29 (m = 5) d̄ = 32 (m = 3) Corollary 1 d̄ = 100 (m = 3) d̄ = 102 (m = 5) d̄ = 107 (m = 5) d̄ = 109 (m = 3)...
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326 citations
Cites background or methods or result from "A New Approach to Stability Analysi..."
...The results in ([28], [29]) were proved to be less and less conservative as the partitioning becomes increasingly thinner for discrete-time T-S fuzzy systems with time-varying delays....
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...Remark 7: Note that [29] is concerned with the state feedback controller design for discrete-time T-S fuzzy systems with time-varying delays, while this work is mainly focused on the problem of the dynamic output controller design....
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...The comparison results are presented in Table I of Example 1, which clearly shows our results are more effective than the work in [29]....
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...To illustrate the effectiveness of the new model transformation, we compare the result in Corollary 1 with Theorem 2 of [29]....
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...This delay partition approach has been used in Theorem 2 of [29]....
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311 citations
284 citations
Cites background or result from "A New Approach to Stability Analysi..."
...which has been considered in [6] and [35]....
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...It can be seen that the methods proposed in this paper are better than the results reported recently in [6] and [35]....
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...Moreover, by comparison of Corollary 1 with some existing ones [6], [26], [35], see Table I in Example 1, it clearly shows our results are more effective than the work in [6], [26], and [35]....
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...Comparing with the existing results to deal with T-S fuzzy time-delay systems, such as the method of circumventing the utilization of some bounding inequalities [6], the input–output approach [26] and the delay partition approach [35], the advantages of our results are twofold....
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...The results in [35] were proved to be less and less conservative as the partitioning becomes increasingly thinner for discrete-time T-S fuzzy time-delay systems....
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References
18,803 citations
"A New Approach to Stability Analysi..." refers background or methods in this paper
...It is well known that there has been a turning point in one of the most effective methods in accordance with the advent of the Takagi-Sugeno (T-S) fuzzy model [19], which is among all of models to solve the control of complex nonlinear systems....
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...Thus, considerable attention has been devoted to investigate nonlinear systems with time-delay by the corresponding T-S fuzzy models [19]....
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3,183 citations
Additional excerpts
...By using the same procedure as in [20], the nonlinear term θ(2) can be exactly represented as θ(2)(k) = h1 (θ(k)) (−m)θ(k) + h2 (θ(k)) mθ(k)...
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1,575 citations
1,099 citations
"A New Approach to Stability Analysi..." refers background or result in this paper
...Some of the existing results were usually derived by using a single Lyapunov function method [21], [24], the main drawback of which is that it leads to conservative results....
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...By using [24], if conditions (33), (34) hold, then (40) is fulfilled....
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...The stability issue of fuzzy control systems has been studied in [8], [21], [24], [26], [29], [30]....
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1,069 citations
"A New Approach to Stability Analysi..." refers background in this paper
...Hence, researchers have been paying remarkable attention to the problems of analysis and synthesis for time-delay systems (for example, [1]–[3], [13], [16], [18], [23], [27], [28], [31], [33], [35], [37])....
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...All these existing literatures for stability analysis can be roughly divided into two types: delay-independent results [23] and delay-dependent ones [13], [16], [27], [35], [37]....
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