{"id":"7312b067-77c0-460d-9d11-883decd4c093","arxiv_id":"2506.02788","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A paper titled for quantized fractional fuzzy systems actually states LMI conditions for a standard integer-order singular T-S fuzzy model, with no fractional, quantized, or event-triggered dynamics in the derivation.","lead":"This paper claims LMI-based stability and filtering conditions for quantized, event-triggered fractional Takagi-Sugeno fuzzy systems with time delays. The equations actually describe an ordinary integer-order singular fuzzy system, and the promised quantization, event-triggering, and fractional operators never appear in the model.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central LMI sufficiency theorem is asserted without proof, and the theorem statements are too garbled to verify; the numerical example cannot close this gap.","rationale":"The reader's weakest_assumption, the unverified membership-derivative bounds rho_i, is a genuine defect in the numerical example, but it presupposes that the theorem itself is sound. The more fundamental problem is that Theorems 1-3 are asserted without proofs and the LMI statements are corrupted, so the sufficiency step cannot be checked at all. I therefore identify the missing proof and unparsable theorem statements as the load-bearing concern. This is not a difference of opinion about modeling conventions; it is an internal gap in the argument. The numerical example cannot repair this gap because it likewise presupposes the theorem, and its own rho_i values are not computed. My recommendation matches the reader's rejection: the paper should not be accepted without a complete, checkable proof of Theorem 2 (and Theorem 3) and a verified choice of rho_i for the example. Hence no verdict adjustment is needed; rejection remains appropriate.","tokens_in":988,"tokens_out":3018,"duration_ms":114811,"concrete_test":"Independently reconstruct the proof of Theorem 2: define the candidate fuzzy Lyapunov-Krasovskii functional, compute its derivative along (21), and verify that (24)-(28) imply ΔV + ν^T ν - γ^2 ω^T ω < 0 for all admissible uncertainties and delay ranges. A specific sub-check is the term Σ_i λ̇_i ζ^T E^T P_i ζ: confirm that Assumptions 3-4 alone bound it, e.g., by rewriting with Σ_i λ̇_i = 0 and using P_i - P_r, and that no additional condition on negative λ̇_i is needed. If the derivation cannot be completed, or if (27) cannot be parsed into a negative-definite block matrix, the central claim is not established. As an auxiliary check, replace rho_1 = rho_2 = 100 in Example 2 with the actual supremum of |2 x_1(t) d(lambda_1)/dt|/9 over the simulated trajectory and re-solve the LMIs; infeasibility would show the numerical validation fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing step is the claimed sufficiency of the LMI conditions in Theorems 2 and 3 for the filtering error system (21). As written, Theorems 1, 2, and 3 are stated without proofs: no Lyapunov-Krasovskii functional is explicitly defined, no derivative computation is shown, and the passage from the membership-function-dependent conditions of Theorem 1 to the strict LMIs (24)-(28) via Assumptions 3-4 is not derived. This matters because the central claim is exactly the conclusion of that sufficiency argument: impulse-freeness, asymptotic stability, and the H-infinity bound for system (21). The statement is also internally uncheckable: condition (27) is typeset as a non-inequality, and the blocks used in (27)-(29) are only partially defined with mismatched dimensions. The recovery formula (30) depends on invertibility and congruence relations among X_i, Y_j, U, W, and their transposes, but no proof of nonsingularity or of the required transformations is given. Consequently the central theoretical claim is unsupported even before considering the numerical example. In the DC motor example, the membership functions are lambda_1 = x_1^2/9 and lambda_2 = 1 - x_1^2/9, giving derivatives 2 x_1 (dx_1/dt)/9, and the chosen bounds rho_1 = rho_2 = 100 are never verified against the simulated trajectory, so the example does not independently validate Assumption 4.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims to solve a quantized dissipative filtering problem for delayed fractional Takagi-Sugeno fuzzy singular systems with time-varying delays under event-triggered networked control, sensor faults, and uncertainties. The plant is modeled as a T-S fuzzy singular system (Eqs. (6), (8)), a filtering error system is formed (Eq. (21)), and Theorems 1-3 assert membership-function-dependent and strict LMI conditions guaranteeing impulse-freeness, asymptotic stability, and an H-infinity performance bound gamma. Controller matrices are to be recovered from Eq. (30). A DC motor/truck-trailer example is used to demonstrate the method. The abstract also promises a unified extended dissipativity framework combining H-infinity, dissipativity, L2-Linfinity, and passivity, although no such combined performance index appears in the main text.","tokens_in":25390,"tokens_out":4512,"duration_ms":43652,"significance":"If the LMI conditions were rigorously proved and the numerical study were an independent validation, the paper would provide a complete reliable H-infinity filter design procedure for a useful class of T-S fuzzy singular systems with random delays. That contribution would be of interest to researchers working on networked fuzzy filtering. However, the central claims are not supported by the text: no proofs are given for Theorems 1-3, the advertised fractional-order and event-triggered/quantization features are not present in the mathematical model, and the membership-derivative bounds on which the LMIs rest are not verified. No reproducible code, machine-checked proofs, or falsifiable parameter-free predictions are supplied. The significance can only be assessed after a full rewrite that supplies the missing derivations and definitions.","major_comments":[{"comment":"The title and abstract promise a 'fractional T-S fuzzy system', but the plant model in Eqs. (6) and (8) and the filtering error system (21) are written with ordinary integer-order derivatives only. No Caputo or Riemann-Liouville derivative, fractional order, or fractional stability notion is introduced anywhere in Section 2. The claimed fractional setting is therefore not actually modeled, and the main theorems cannot be read as results about fractional systems.","section":"Section 2, Eqs. (6) and (8)"},{"comment":"Theorems 1, 2, and 3 are stated as assertions but no proofs are given. There is no Lyapunov-Krasovskii functional, no computation of its derivative, and no derivation of the transition from the membership-function-dependent conditions of Theorem 1 to the strict LMIs (24)-(28) via Assumptions 3-4. In addition, condition (27) is typeset as a non-inequality with undefined blocks, and the matrices in (27)-(29) are only partially defined with mismatched dimensions. The recovery formula (30) assumes nonsingular matrices U and W satisfying congruence relations without any proof of existence or invertibility. Thus the central sufficiency claim is unverifiable as written.","section":"Section 3, Theorems 1-3"},{"comment":"The abstract and contribution list state that an event-triggered scheme and logarithmic quantization are implemented and that the quantization effect is transformed into induced communication delays. However, no event-triggering condition, no quantization map, no sector-bound representation, and no delay-induction argument appear in Section 2 or in the problem formulation. The system used in Theorems 1-3 does not contain any quantization or event-triggering variables; consequently the claimed results do not cover the advertised network control mechanism.","section":"Abstract and Section 2.3"},{"comment":"The numerical validation is not independent. In Example 2 the parameter gamma is fixed to 1.5 and the LMIs are reported feasible, which is only a consistency check on a chosen parameter, not a computation of minimal gamma or a falsifiable prediction. Table 2 compares minimal gamma values with [61], [63], [65], and [67], but the rows labeled 'Corollary 1' report only orders of magnitude (10^-3, 10^-2, ...) with no explicit values or problem data, so the claimed less conservatism is not checkable. Furthermore, Assumption 4 requires bounds rho_i on the membership-function derivatives h_i, and the chosen rho_1 = rho_2 = 100 are never verified against the simulated trajectory; if these bounds fail, the sufficiency of the LMIs is void.","section":"Section 4, Table 2 and Example 2"}],"minor_comments":[{"comment":"The manuscript contains many corrupted formulas and typos ('ABSTARCT', 'asymptomatically stable', 'associative Lyapunov'), which make it hard to parse; a full editorial cleanup is needed.","section":"Throughout"},{"comment":"Table 3 and Table 4 are identical but labeled differently, and Figure captions 5-6 refer to states and the truck-trailer system without matching the example numbering.","section":"Tables 3 and 4"},{"comment":"The notation section is incomplete: several symbols used in Theorems 1-3, such as hat(P)_i, Gamma_ij, Xi_ij, and the scalar a_k, are not fully defined.","section":"Notations"},{"comment":"Assumption 3 is stated with an incomplete inequality and no explicit relation to the membership functions, and the relationship between Assumption 3 and Assumption 4 is unclear; this should be corrected if the manuscript is revised.","section":"Assumptions 3 and 4"},{"comment":"Some references have malformed DOIs or incomplete bibliographic data (e.g., reference [9] contains 'https://doi.org/110.1109/TAC.2011.2178629'), and references [62]-[68] are not consistently formatted.","section":"References"}],"recommendation":"reject","confidential_remarks":"The manuscript is not ready for review in its current form: the main technical content is a sequence of asserted LMI conditions with no derivations, and the title's fractional and event-triggered/quantization components are not present in the model. The numerical example is a consistency check rather than an independent validation. I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper reads like a standard LMI design for singular T-S fuzzy systems with random delays, but the title and abstract promise much more: fractional calculus, quantization, event-triggered communication, and extended dissipativity. None of those features actually show up in the model. The equations in (6)-(8) are the usual integer-order singular T-S system, and the rest of the paper follows the familiar Lyapunov-Krasovskii plus LMI template. There is no fractional operator defined, no event-triggering condition stated, and no quantization map anywhere in the derivation. So the central claim, that this is a quantized dissipative fractional framework, is not supported by the text.\n\nWhat the paper does reasonably well: the literature review is broad, and the DC motor motivation is concrete. The LMI problem is set up in the standard way, and the authors correctly identify the relevant performance indices. If the theorems were proven, the recovery formula (30) would be a plausible way to extract controller gains from feasible LMIs. But that is where the problems start.\n\nThe main soft spots are load-bearing. Theorems 1, 2, and 3 are stated without proofs. No Lyapunov-Krasovskii functional is explicitly defined, no derivative computation is shown, and the step from membership-function-dependent conditions to strict LMIs via Assumptions 3 and 4 is not derived. Condition (27) is typeset as a non-inequality, and the blocks in (27)-(29) have mismatched dimensions and are only partially defined. Assumptions 3 and 4 assert bounds on membership function derivatives, but for the DC motor example the membership functions are lambda_1 = x_1^2/9 and lambda_2 = 1 - x_1^2/9; the chosen bounds rho_1 = rho_2 = 100 are never verified against the simulated trajectory. The numerical comparison includes a mysterious \"Corollary 1\" row with gamma values near 10^-10 that is never explained, and Figure 1's caption references a truck-trailer model that is never simulated. These are not minor copyediting issues; they remove the evidential basis for the claimed result.\n\nWho is this for? A reader who wants a one-stop citation for LMI-based H-infinity filtering of singular T-S systems with random delays might skim the introduction, but they would be misled about what is actually derived. The paper does not deserve a serious referee in its current state. My recommendation: desk reject, and ask the authors to resubmit only if they rewrite the paper with the advertised features actually modeled, complete proofs, and a reproducible numerical study that verifies the assumptions.","headline":"The advertised fractional, quantized, event-triggered framework never appears in the equations, and the central LMI theorems are stated without proof; this paper is not ready for peer review.","tokens_in":25952,"tokens_out":2152,"would_cite":false,"duration_ms":21147,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["93C42","93C23","93B36","93D30"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that one set of LMI feasibility conditions guarantees a filter for delayed Takagi-Sugeno fuzzy singular systems that keeps the filtering error impulse-free and asymptotically stable under sensor faults, event-triggered…","keywords":["T-S fuzzy systems","singular systems","time-varying delays","H-infinity filtering","event-triggered control","quantization","sensor faults","linear matrix inequalities"],"falsifier":"Simulate the DC motor example with the given disturbances and uncertainties, record the maximum of $|\\dot h_i(t)|$ for the membership functions in (37) along the trajectory, and compare it with the chosen $\\rho_i$ (the simulations set $\\rho_1=\\rho_2=100$). If any realized derivative exceeds the assumed bound, Assumption 4 is violated for that run and the LMI-certified guarantee does not apply; if the bound holds, the numerical demonstration is consistent with the theorem.","tokens_in":24868,"feed_emoji":"📡","tokens_out":12230,"duration_ms":109842,"temperature":0.7,"pith_summary":"This paper tries to establish a complete filter-design recipe for a nonlinear plant modeled as a Takagi-Sugeno fuzzy singular system with time-varying delay, parameter uncertainty, sensor faults, and a network that sends measurements only when an event-triggered condition fires and then quantizes them logarithmically. The recipe is a set of linear matrix inequalities (LMIs): if a computer can find matrices satisfying inequalities (24)-(28) and (31), then the paper claims the filtering error system is impulse-free and asymptotically stable with prescribed noise-rejection level $\\gamma$, and equations (30) hand back the filter matrices. The reason to care is practical: in networked control, delays, data reduction, and faulty sensors are the norm, so a filter that provably tolerates all three at once is directly usable. The paper demonstrates the design on a nonlinear DC motor model and reports smaller minimal $\\gamma$ than four earlier T-S fuzzy filter designs for the same delay bounds.","feed_headline":"One LMI check proves a fuzzy filter stable on lossy channels","feed_subtitle":"For delayed T-S fuzzy systems with sensor faults and quantization, one feasibility test yields a guaranteed noise-rejection level.","key_machinery":"The engine of the proof is a fuzzy Lyapunov-Krasovskii functional: a Lyapunov function built from fuzzy-membership-dependent matrices plus single and double integral terms over the delay intervals, which converts the stability and dissipativity requirement into matrix inequalities. Randomness of the delays is encoded by a Bernoulli variable that splits the delay into two distributions (Assumptions 1-2), the sensor faults enter through a diagonal fault matrix $\\beta$ in (16)-(18), and the quantized event-triggered channel is folded into the error dynamics as communication-induced delay. Theorems 2 and 3 then linearize the general conditions by assuming bounds $\\rho_i$ on the membership-function derivatives $h_i$, producing strict LMIs; equations (30) recover the filter gains.","core_discovery":"The paper claims that Theorems 2 and 3 give sufficient conditions for the existence of a resilient delayed singular fuzzy filter for system (8): under Assumptions 3 and 4, feasibility of the LMIs (24)-(28) and (31) guarantees that the filtering error system (21) is impulse-free and asymptotically stable with $H_\\infty$ performance level $\\gamma$, for any time-varying delays satisfying Assumption 2 and uncertainties of the linear-fractional form (7). The filter matrices are then recoverable from equations (30). This extends earlier T-S fuzzy $H_\\infty$ filter designs to a setting that simultaneously includes sensor faults, event-triggered transmission, logarithmic quantization, random time-varying delays, and a unified dissipativity requirement covering $H_\\infty$, passivity, $L_2$-$L_\\infty$, and purely dissipative performance.","pith_inferences":["The simulation uses $\\rho_1=\\rho_2=100$ without a computed bound on $\\dot h_i$ along the actual trajectories; a reader who wants a theorem-guaranteed filter would need to verify these bounds from the operating region or the state equations.","The comparison in Table 2 is against delay-free $H_\\infty$ T-S filter designs without sensor faults, quantization, or event triggering; the reported $\\gamma$ improvements therefore measure the new delay-dependent machinery, not the cost or benefit of the extra networked features.","The title calls the systems fractional, but the state equations (6), (8), (15), and (21) use ordinary integer-order derivatives; applying the design to a genuinely fractional-order plant would require a separate derivation.","A natural next experiment is to run the recovered filter on a networked DC motor emulator that drops and quantizes measurements, and compare the measured $L_2$ gain of the estimation error with the predicted $\\gamma$."],"forward_implications":["Feasible LMIs certify a filter for the full networked setting, so a designer can check stability and noise rejection with one numerical test before implementation.","The recovered filter matrices give an explicit controller (19) whose error system rejects disturbances with level $\\gamma$ despite sensor faults and packet-saving communication.","The unified dissipativity setup means one theorem covers $H_\\infty$, passivity, $L_2$-$L_\\infty$, and dissipative performance as special cases, so a single feasibility run serves multiple design specs.","For the DC motor example, the reported minimal $\\gamma$ drops from the 0.31-2.22 range of four earlier T-S fuzzy filters to $10^{-3}$-$10^{-2}$, indicating less conservative delay-dependent conditions.","The method extends to any plant that admits a T-S fuzzy singular model with bounded membership-derivative rates, not just the DC motor and truck-trailer examples used for simulation."],"supporting_citations":[{"why":"Supplies the baseline T-S fuzzy $H_\\infty$ filter design whose minimal $\\gamma$ values Table 2 compares against.","marker":"[61]"},{"why":"Another prior T-S fuzzy $H_\\infty$ filter design used as a comparison baseline in Table 2.","marker":"[63]"},{"why":"Prior delay-dependent T-S fuzzy $H_\\infty$ filter design whose reported $\\gamma$ values this paper claims to improve.","marker":"[65]"},{"why":"Directly prior $H_\\infty$ fuzzy filtering result for nonlinear singular systems with time-varying delay, extended here to the fault and quantized networked setting.","marker":"[67]"},{"why":"Supplies the linear-fractional uncertainty representation (7) used for both the plant and controller parameter uncertainties.","marker":"[52]"},{"why":"Provides the probability-distribution model for random time delays formalized in Assumptions 1 and 2.","marker":"[55]"},{"why":"Source of the sensor-failure model with the diagonal fault matrix $\\beta$ used in (16)-(18).","marker":"[57]"},{"why":"Earlier quantized dissipative filter design for T-S fuzzy systems that the present quantization and dissipativity framework builds on.","marker":"[58]"}],"fun_headline_variants":["Feasible LMI set yields resilient fuzzy filter for delayed T-S systems","Quantized fuzzy filtering stable under delays via one LMI feasibility test","Resilient filter for T-S fuzzy networks with quantization and faults from LMIs","One LMI check guarantees dissipative filtering for fractional T-S systems"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The guarantee rests on the assumption that the fuzzy membership functions never change faster than the chosen rates $\\rho_i$, yet the paper states those rates for the example without computing them from the dynamics; if the actual rates are larger, the LMI conditions are not sufficient and the filter is not guaranteed.","fun_headline_variants_meta":{"raw":{"variants":["Feasible LMI set yields resilient fuzzy filter for delayed T-S systems","Quantized fuzzy filtering stable under delays via one LMI feasibility test","Resilient filter for T-S fuzzy networks with quantization and faults from LMIs","One LMI check guarantees dissipative filtering for fractional T-S systems"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00054,"raw_usage":{"total_tokens":2569,"prompt_tokens":907,"completion_tokens":1662,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":523,"completion_tokens_details":{"reasoning_tokens":1582}},"tokens_in":523,"tokens_out":1662,"duration_ms":11907,"temperature":1.0,"reasoning_tokens":1582,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:16:11.970898+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the DC motor example with the given disturbances and uncertainties, record the maximum of $|\\dot h_i(t)|$ for the membership functions in (37) along the trajectory, and compare it with the chosen $\\rho_i$ (the simulations set $\\rho_1=\\rho_2=100$). If any realized derivative exceeds the assumed bound, Assumption 4 is violated for that run and the LMI-certified guarantee does not apply; if the bound holds, the numerical demonstration is consistent with the theorem.","supporting_citations":[{"cited_title":"Lin, Q.G","cited_arxiv_id":null,"evidence_quote":"Supplies the baseline T-S fuzzy $H_\\infty$ filter design whose minimal $\\gamma$ values Table 2 compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Another prior T-S fuzzy $H_\\infty$ filter design used as a comparison baseline in Table 2."},{"cited_title":"Huang, X.-Q","cited_arxiv_id":null,"evidence_quote":"Prior delay-dependent T-S fuzzy $H_\\infty$ filter design whose reported $\\gamma$ values this paper claims to improve."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the linear-fractional uncertainty representation (7) used for both the plant and controller parameter uncertainties."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the probability-distribution model for random time delays formalized in Assumptions 1 and 2."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Source of the sensor-failure model with the diagonal fault matrix $\\beta$ used in (16)-(18)."},{"cited_title":"Quantized dissipative filter design for Markovian switch T–S fuzzy systems with time -varying delays, Soft Computing , https://doi.org/10.1007/s00500-019- 03884-w, vol","cited_arxiv_id":null,"evidence_quote":"Earlier quantized dissipative filter design for T-S fuzzy systems that the present quantization and dissipativity framework builds on."}],"review_version":1}