The chaotic propagation of computer viruses presents a significant challenge in cybersecurity, necessitating advanced mathematical models for understanding and controlling their spread. In this study, we investigate the stabilization and synchronization of chaos in a fractional-order discrete computer virus model with incommensurate order. We begin by analyzing the chaotic behavior of the incommensurate fractional virus model, thereby employing tools such as bifurcation diagrams, phase portraits, and Lyapunov exponents to characterize its nonlinear dynamics. The results reveal that the system exhibits chaotic behavior under specific parameter conditions, which results in unpredictable virus spread. To mitigate these chaotic effects, we implement stabilization strategies aimed at stabilizing the system and suppressing chaotic outbreaks. Additionally, we explore synchronization techniques, which are of paramount importance in understanding virus interactions within networked systems. Numerical results are presented to corroborate the theoretical findings presented in this paper.

The stabilization problem of a class of fuzzy systems with particular uncertainty restrictions is addressed in this paper using an observer design. We construct a fuzzy controller that ensures the Takagi-Sugeno fuzzy systems' uncertain solutions will converge. The ability to examine the convergence of trajectories using an estimated state controller towards a certain region of the origin that defines the system's asymptotic behavior is one benefit of the methodology employed in this work. Additionally, we provide an example to demonstrate the primary result's validity.

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.

This paper aims to design Observer-Based (OB) controllers that ensure the exponential stability of a class of nonlinear time-delay systems. The nonlinear part of the system satisfies a weak Quasi-One-Sided Lipschitz (QOSL) condition characterized by the matrices $({\mathcal{L}}_1,{\mathcal{M}}_1,{\mathcal{N}}_1)$, as well as a QOSL condition characterized by the matrices $({\mathcal{L}}_2,{\mathcal{M}}_2,{\mathcal{N}}_2)$. First, we derive a sufficient condition formulated as a Linear Matrix Inequality (LMI) via a Lyapunov–Krasovskii (LK) functional. The main advantage of this design is that the controller and observer gains are computed in a single step. However, its main drawback is that the matrices ${\mathcal{L}}_1$, ${\mathcal{M}}_1$, and ${\mathcal{N}}_1$ are fixed rather than treated as decision variables. To overcome this limitation, we propose an improved design in which the matrices ${\mathcal{L}}_1,{\mathcal{M}}_1$, and ${\mathcal{N}}_1$ are treated as decision-variable matrices with a fixed structure. By using an appropriate decoupling technique, this approach provides greater flexibility in the selection of matrices and reduces conservatism. The efficacy of the developed OB controllers is demonstrated via a suitable numerical example.

This study investigates how to control chaos in discrete-time systems that have variable fractional orders. We examine a general type of discrete fractional-order equations where the order changes with time, and we show that these systems can become chaotic when certain parameters are chosen. To address this, we develop and apply tailored control techniques to suppress chaos and achieve system stabilization. Using detailed numerical simulations, we confirm that the suggested control method works effectively in two example cases. Our findings underscore that chaos control in variable fractional-order systems provides significant flexibility in modulating dynamic behavior, offering valuable insights into the broader applicability of these methods in discrete fractional-order systems.

In this research, we present a novel discrete fractional-order model designed to simulate computer virus propagation. We performed a thorough dynamical analysis, encompassing phase portrait visualization, bifurcation diagram construction, maximal Lyapunov exponent computation, and equilibrium point stability assessment using the basic reproduction number ( $R_0$). To characterize system complexity and validate chaotic dynamics, we employed Approximate Entropy, $C_0$ Complexity, and Permutation Entropy. Furthermore, control and synchronization methodologies were developed to mitigate chaotic behavior and achieve coordinated system dynamics. The findings proved the efficacy of the proposed fractional model in accurately simulating viral spread and illustrated the considerable implications of fractional-order parameters on system dynamics. In order to validate the results, MATLAB simulations were run.