Drug Database
LK

LKF (Pentadecan / LKF / PDG)

✓ Approved

Lion · Small Molecule · Small Molecule

What is LKF?

LKF is a small molecule developed by Lion. It is approved for therapeutic indications.

Drug Profile

Brand NamesPentadecan, LKF, PDG
CompanyLion
Drug ClassSmall Molecule
StatusApproved
Sources: ClinicalTrials.gov, Lion

Therapeutic Indications

LKF is developed for 2 unique indications across 1 therapeutic area.

Therapeutic AreaConditionPhase
Skin and subcutaneous tissue disordersSkin disorder✓ Approved
Skin and subcutaneous tissue disordersDermatosis✓ Approved

Related Research Articles

PubMedISA transactions2026-11-04

Robust fractional hybrid controller for frequency regulation in nonlinear multi-area power systems amid communication delay and cyber-attack.

Ansari Zafar Ayub ZA, Ali Mohammed Hasmat MH, Arya Yogendra Y, Raja G Lloyds GL

The digitalization of modern power systems (PSs) has transformed conventional grids into cyber-physical systems, increasing their vulnerability to communication delays and signal disturbances. This paper proposes a Flow Direction Algorithm (FDA)-optimized one-plus-tilt derivative cascaded with a fractional-order integral-derivative ((1+TD)-IλDμ) controller for robust load frequency control of nonlinear renewable-integrated PSs. The cascaded fractional-order structure enhances tuning flexibility and robustness against communication delays and signal perturbations. Rather than detecting cyber-attacks (CAs), the proposed controller is evaluated under false data injection (FDI), denial-of-service (DoS) attacks, random communication delays, and hybrid CAs using multiple benchmark PS models. A unified controller tuning strategy is employed across all operating scenarios, including the IEEE 39-bus and Kundur 11-bus test systems. Stability is verified through the Lyapunov-Krasovskii functional (LKF)-linear matrix inequality (LMI) framework, while controller-in-the-loop (CIL) experiments confirm the controller's practical feasibility and real-time applicability.

PMID 42982676
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PubMedISA transactions2026-10-29

An improved bivariate quadratic function negative-definiteness lemma for trajectory tracking of T-S fuzzy 2-DOF helicopter systems with two additive time-varying delays.

Zhu Tingyi T, Ren Jiaojiao J, Shi Kaibo K

This paper investigates the delay-dependent stability and trajectory-tracking control of a nonlinear two-degree-of-freedom (2-DOF) helicopter system with two additive time-varying delays. An improved partially linearized Takagi-Sugeno (T-S) fuzzy model is developed to retain the key pitch-angle nonlinearities while avoiding the excessive simplification of full linearization and maintaining tractability. To handle the bivariate quadratic terms in the derivative of the Lyapunov-Krasovskii functional (LKF), an improved bivariate quadratic negative-definiteness lemma with tunable parameters is proposed. Based on this lemma, a delay-dependent stability criterion and a fuzzy PID controller design method are derived, where the tunable parameters are determined offline by a Bayesian-optimization-based algorithm. Numerical examples show that the proposed method yields a larger allowable delay upper bound (ADUB) and achieves effective trajectory tracking under time-varying delays.

PMID 42951746
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PubMedPloS one2026-08-07

Multi-rate sampled-data control for T-S fuzzy systems with mismatched fuzzy basis functions.

Nguyen Khanh Hieu KH

This paper investigates a multi-rate sampled-data (MRSD) stabilization criterion for T-S fuzzy systems with the consideration of mismatched fuzzy basis functions (FBFs). To fully exploit the system information under a MRSD mechanism, we incorporate an improved looped-functional and a discontinuous function into the Lyapunov-Krasovskii functional (LKF). This construction explicitly leverages the most recent measurements and the sampling-induced delay associated with each system state. Furthermore, to address a set of conditions expressed as parameterized linear matrix inequalities (PLMIs), this paper develops a refined relaxation technique for mismatched FBFs that explicitly exploit their inherent properties. Finally, two examples are provided to demonstrate the effectiveness and practicality of the proposed method.

PMID 42566451
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PubMedIEEE transactions on cybernetics2026-06-16

Improved Passivity Analysis for Neural Networks With Time-Varying Delay.

Zhou Xi-Zi XZ, An Jianqi J, He Yong Y

This article presents the passivity analysis of neural networks with time-varying delays (NNTVDs). The primary challenge stems from nonlinear delay-dependent terms that arise in estimating the derivative of the Lyapunov-Krasovskii functional (LKF). To address this, a linearization variable augmentation method is developed that strategically employs zero equations in conjunction with time-varying free-weighting matrices incorporating the delay derivative. This novel formulation completely eliminates nonlinear delay terms, rendering the passivity condition affine with respect to the delay. Furthermore, an improved time-varying S-procedure is proposed, where the multiplier matrices are constructed as affine functions of the delay, its derivative, and their product, providing greater freedom for bounding the neuron activation functions. These two key innovations together yield novel passivity and stability criteria that are significantly less conservative than existing ones, as rigorously demonstrated by comparative numerical examples and a practical case study.

PMID 42301833
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PubMedNeural networks : the official journal of the International Neural Network Society2026-06-15

Relaxed conditions and PSO-based optimization for the problem of Mittag-Leffler synchronization and its application in image restoration for fractional-order octonion-valued two-layer neural networks.

Xiao Jianying J, Huang Benkun B, Wen Shiping S

This study focuses on Mittag-Leffler synchronization of fractional-order octonion-valued two-layer neural networks (FOOVTLNNs) and its application in color image restoration. The non-commutativity and non-associativity of octonion algebra and memory-dependent dynamics of fractional-order systems pose key challenges for low-conservative synchronization criteria and efficient optimization. A unified FOOVTLNNs' model is established via Caputo fractional derivatives and general activation functions. A novel fractional-order quadratic inequality in octonion field is derived to reduce conservatism, and a hybrid framework such as non-decomposed Lyapunov-Krasovskii functional(LKF) and real-component-separated deduction is proposed to handle octonion algebraic constraints. Quadratic coefficients are embedded into LKF, criteria and controller gains for joint constraint relaxation. Particle swarm optimization (PSO) optimizes the quadratic coefficients, and three PSO-based synchronization algorithms are designed. Numerical simulations and image restoration experiments validate the method that the optimized algorithms can reduce conservatism, accelerate convergence, and improve Peak Signal-to-Noise Ratio (PSNR) and so on. The hybrid strategy overcomes some limitations of fractional-order octonion-valued network, while the relaxed criteria and PSO-aided algorithms provide a reliable theoretical and practical basis for FOOVTLNN synchronization and multimedia applications.

PMID 42287981
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PubMedIEEE transactions on cybernetics2026-06-08

Passivity-Based Pinning Synchronization Control of Switched Directed Networks With Improved Switching Strategy.

Cui Chongyi C, Sang Hong H, Liu Yi Y, Wang Peng P et al.

This research delves into the passivity-based pinning synchronization problem for switched directed networks (SDNs) within the context of a sampled-data-based event-triggered (SDET) communication environment. An improved state-dependent switching strategy (SDSS) using sampled measurements alongside a novel time-dependent Lyapunov-Krasovskii functional (LKF) approach is constructed. Subsequently, a relaxed passivity analysis framework is then presented, ensuring that the resultant synchronization error system (SES) remains passive, and that the examined SDNs achieve asymptotic synchronization in the absence of external inputs. Unlike conventional strategies, the proposed switching protocol depends exclusively on system states at discrete sampling instants and effectively utilizes historical state data, yielding a less conservative theoretical framework for passivity synthesis in SDNs. Furthermore, the resulting synchronization criterion is independent of the number of network nodes, rendering it suitable for SDNs with large size. Ultimately, two examples involving relevant application in image encryption and decryption are provided to verify the effectiveness and applicability of the proposed scheme, and highlight the distinct advantage of switching behaviors in enhancing encryption confidentiality.

PMID 42258674
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