This paper introduces novel input-to-output stability concepts, namely fractional exponential input-to-output practical stability (FE-IOPS) for conformable fractional-order systems. We establish sufficient Lyapunov conditions to ensure these stability properties in nonlinear fractional systems with conformable derivatives. Additionally, we investigate the practical stability of fractional exponential output in nonlinear fractional-order systems without external input. Building on these results, we analyze the FE-IOPS of perturbed conformable fractional-order systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed methodology.
In this abstract, we discuss some of the key results and techniques related to the commutativity of fractional-order LTVSs, including the use of linearity, time-varying behavior, fractional-order dynamics, and commutative conditions. These conditions must be satisfied in order for commutativity to hold for these systems. However, the commutativity of fractional-order LTVSs has not been widely explored. In this paper, we explore the properties of these systems and their ability to commute. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. The findings and results are presented for the first time since it is not present yet in the literature and have unlimited applications for the design and control of fractional-order systems in practical applications.
This article focuses on the stability analysis of fractional-order derivative for nonlinear Chen chaotic systems using Caputo–Fabrizio fractional derivative. The primary objective is to examine the criteria for existence and uniqueness using the fixed-point technique. The study explores Ulam stability results and discusses other significant findings for the proposed system. Numerical schemes are employed using Lagrange polynomial interpolation with Caputo–Fabrizio fractional derivative. Simulated graphical representations are generated for different fractional-order values, and the simulation results validate the efficacy and practical applicability of the theoretical findings.
This paper addresses the finite time stability (FTS) of proportional fractional Itô–Doob stochastic systems with time delays. It begins by defining the key concepts and mathematical formulations necessary for understanding these systems. The main contributions include the derivation of sufficient FTS conditions using some mathematical inequalities, which integrates proportional fractional calculus, stochastic analysis, and time-delay compensation. The paper also presents an example to verify the theoretical bounds. The findings provide a comprehensive perspective on stochastic fractional control, highlighting the importance of addressing time delays and stochasticity in fractional-order systems.
This paper focuses on addressing the challenges of finite-time output tracking control for unmanned aerial vehicles (UAVs) with a particular emphasis on security concerns. The potential impact of denial-of-service (DoS) attacks on the integrity of measurement-to-control communication channels is incorporated into our analysis. Such attacks may disrupt the central control unit's capability to access real-time measurement data, which encompasses the system states and the reference signal information. Under this consideration, we have formulated sufficient conditions based on the Lyapunov theory, aimed at ensuring that the system's state trajectory remains confined within a pre-established boundary over a designated time frame. However, note that there are some coupling terms of unknown matrix variables, and the developed conditions are nonlinear and difficult to be solved by some commonly used linear matrix inequality (LMI) techniques. In order to handle the nonlinear and non-convex constraints in the determination of the controller gains and the finite-time performance, we have proposed a novel iterative algorithm. The novel presented algorithm mainly combines genetic algorithm with LMI techniques. To validate the effectiveness of our approach, a case study of a UAV networked output tracking control system is conducted and detailed in the final section of this paper.
This work focuses on developing a mode-dependent estimator for neural networks that have semi-Markov jump parameters and sensor nonlinearities under the imperfect network environment. Semi-Markov jump process with its unique superiority is employed to depict mode switching within neural networks. The data sent over a communication network are considered to be at risk of cyber-attacks, where adversaries could introduce false data in a probabilistic manner. Due to complex practical situations, the sensor may exhibit nonlinear characteristics. A state estimator is utilized to produce estimates for the underlying neural networks, incorporating the sensor's nonlinear characteristics. Furthermore, an applicable estimator is devised by addressing the convex optimization problem. Lastly, the efficacy of the formulated estimator is demonstrated through a numerical illustration.
In this paper, the fault detection problem of event-triggered distributed multi-agent systems is addressed using the optimization approach. Owing to the active packet loss behavior of the event-triggered mechanism, the event-triggered transmission error which is the error between the data of the nontriggered time and current actual time is inevitable. Firstly, the multi-agent systems model with event-triggered mechanism is represented by the variable sampling period method. Subsequently, the distributed fault detection filter with optimization for the multi-agent systems model is developed to decouple the event-triggered transmission error from the residual signal. Meanwhile, the optimum solution of the fault detection filter is given, and the state estimation error convergence is analyzed. Finally, the comparing simulations are given to verify the effectiveness and feasibility of the proposed method in the multi-agent systems composed of four F-18 aircrafts.
Fractional calculus, particularly the conformable fractional derivative, has gained significant attention for its ability to extend classical differentiation to noninteger orders while preserving essential properties and incorporating memory effects into system models. This paper focuses on the stability analysis of triangular systems characterized by generalized conformable derivatives, leveraging their partitioned structure to simplify analysis. By constructing a Lyapunov-like function tailored to the generalized conformable derivative framework, we derive sufficient conditions for practical uniform stability and asymptotic convergence of system states, even in the presence of nonlinear perturbations and parameter variations. Unlike previous works that rely on the Caputo derivative, our approach employs the generalized conformable derivative, overcoming its limitations and extending the analysis to a broader class of nonlinear systems. This generalization enhances both theoretical robustness and practical applicability, offering more flexible stability criteria for complex systems. The paper concludes with illustrative examples and future research directions, highlighting the framework's potential to advance fractional-order stability analysis.
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