This paper investigates the finite-time boundedness (FBss) of perturbed nonlinear systems with interval time-varying delay. First, the system's nonlinear dynamics are represented by a Takagi–Sugeno (TS) fuzzy model, while quasi-one-sided Lipschitz (QL) terms account for either intrinsic nonlinearities or lumped uncertainties. This formulation captures a broad class of systems, encompassing both natural system nonlinearities and aggregated perturbations. Second, to ensure the FBss of the proposed system, an observer-based controller (OC) is employed under the assumption that the premise variables are measurable, even if the QL condition itself involves unmeasurable states. Then, a single-step procedure based on linear matrix inequalities (LMIs) is proposed to design the OC gains. To this end, a Lyapunov–Krasovskii (LK) functional is employed, comprising a delay-free quadratic term, which incorporates the matrix $\mathcal{P}$ used to verify the QL condition, along with three integral terms that capture the effects of the interval time-varying delay, including its lower and upper bounds. In addition, we employ a suitable decoupling approach that allows $\mathcal{P}$ to be regarded as a full decision-variable matrix and enabling the LMI conditions to be derived in a single step. The effectiveness and feasibility of the proposed methods are finally verified through a simulation study.

This paper develops an incommensurate fractional-order susceptible-exposed-symptomatic infectious-asymptomatic infectious-treated-recovered (SEIATR) model with compartment-specific Caputo memory. We establish local well-posedness, positivity, boundedness, biological feasibility, disease-free and endemic equilibria, and the basic reproduction number. Local stability is analyzed through the rational-order incommensurate Matignon criterion. A componentwise multi-order L1 scheme is then used for simulation, refinement, and sensitivity analysis. Finally, a physics-informed neural network is employed as a synthetic benchmark for hidden-state reconstruction, parameter and order identification, residual checking, and short-horizon forecasting. The results show that compartment-specific memory mainly affects peak timing, persistence, and treatment load, whereas epidemiological rates govern amplification and threshold behavior.

This paper proposes a distributed finite-time coordination and tracking control framework for partially shaded photovoltaic (PV) arrays. The considered architecture combines a sampled-data outer coordination layer with a continuous-time inner tracking layer in order to improve global power extraction under nonuniform irradiance conditions. At the local level, each PV submodule is equipped with an artificial neural network (ANN) that provides a fast estimate of a baseline operating voltage from irradiance and temperature measurements. To move beyond purely local maximum power point tracking (MPPT) operation, a distributed finite-time observer is developed so that every agent reconstructs the sampled total array power using only neighbor-to-neighbor communication. Based on this shared information, a cooperative projected-ascent command-update law is introduced to refine the ANN initialization and generate improved voltage commands through a regularized sampled objective. In the inner loop, a reference filter and a robust sliding-mode controller are designed to guarantee accurate voltage tracking despite bounded modeling uncertainty and disturbances. Theoretical outputs determine the possibility of finite-time recovery of the sampled total power, the monotonicity and stationarity of the distributed command-update law, and the finite-time convergence to the sliding manifold and exponential tracking of the filtered command. Simulation studies carried out on a four-agent partially shaded PV array confirm the effectiveness of the proposed framework. Specifically, the distributed observer converges within the prescribed coordination interval, the cooperative outer layer monotonically improves the sampled cooperative objective, and the overall closed-loop architecture delivers an average power gain of $13.4079$ across the tested irradiance scenarios. These findings indicate that the proposed distributed architecture provides a flexible and reliable solution for cooperative MPPT in partially shaded PV systems.