Controllability and Observability of Fractional Linear Systems with Two Different Orders

Xu, Dengguo; Li, Yanmei; Zhou, Weifeng

doi:10.1155/2014/618162

Cited by 12 publications

(6 citation statements)

References 19 publications

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“…Li et al [26] studied the controllability of RL fractional delay differential equations. In [27], the authors explored the controllability and observability of fractional linear systems, described by the Caputo derivative with distinct orders. From our review of the literature, there appears to be a gap in studying the controllability for two types of different local fractional (LF) systems.…”

Section: θ(T)mentioning

confidence: 99%

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

Awadalla,

Chaouk,

Jneid

et al. 2024

Fractal Fract

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In this paper, we investigate the controllability conditions of linear control systems involving distinct local fractional derivatives. Sufficient conditions for controllability using Kalman rank conditions and the Gramian matrix are presented. We show that the controllability of the local fractional system can be determined by the invertibility of the Gramian matrix and the full rank of the Kalman matrix. We also show that the local fractional system involving distinct orders is controllable if and only if the Gramian matrix is invertible. Illustrative examples and an application are provided to demonstrate the validity of the theoretical findings.

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Section: θ(T)mentioning

confidence: 99%

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

Awadalla,

Chaouk,

Jneid

et al. 2024

Fractal Fract

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“…If the system reaches X(t) = X f within a finite time or a finite concentration t for any given initial state x o and any given final state X f . According to Wang and Liu (2011) and Xu et al (2014) the system can be reversed and intervened. The system dynamics or concentration gradient equation is: Y = A x + B u x ∈ R N , u ∈ R N…”

Section: Strategymentioning

confidence: 99%

Network Intervention, a Method to Address Complex Therapeutic Strategies

et al. 2018

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Objective: Network-based approaches emerged as powerful tools for studying complex diseases. Our intention in this article was to raise awareness of the benefits of new therapeutic strategy in biological networks context and provide an introduction to this topic.Methods: This article will discuss the rational for network intervention, and outline some of the important aspects of deciphering targets activities in the network and future embodiments of network intervention. We also present examples of network intervention based on the strategies these approaches use.Results: Network intervention seeks for target combinations to perturb a specific subset of nodes in disease networks to inhibit the bypass mechanisms at systems level. Experimental results derived from our studies are discussed, with conclusions that lead to future research directions. A simple diagram is designed to give a way to find the minimum number of external input required for a network intervention based on the graph theory and get the analytical value of the least input.Conclusion: Creating network intervention that addresses blindness and unthinking action in this way could, therefore, provide more benefit than multi-target therapy. We hope that this article will give readers an appreciation for a new therapeutic strategy that has been proposed for improving clinical benefit by adopting network-based approaches as well as insight into their properties.

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“…where H is an appropriate order matrix. In [30], the authors have established some results for the controllability and observability of a linear system with non-integer distinct orders. Their proposed dynamical system is as follows:…”

Section: Introductionmentioning

confidence: 99%

Controllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical System

Ahmad

Rahman

et al. 2022

Mathematics

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Recently, several research articles have investigated the existence of solutions for dynamical systems with fractional order and their controllability. Nevertheless, very little attention has been given to the observability of such dynamical systems. In the present work, we explore the outcomes of controllability and observability regarding a differential system of fractional order with input delay. Laplace and inverse Laplace transforms, along with the Mittage–Leffler matrix function, are applied to the proposed dynamical system in Caputo’s sense, and a general solution is obtained in the form of an integral equation. Then, we set out conditions for the controllability of the underlying model, regarding the linear case. We then expound controllability conditions for the nonlinear case by utilizing the fixed point result of Schaefer and the Arzola–Ascoli theorem. Using the fixed point concept, we prove the observability of the linear case using the observability Grammian matrix. The necessary and sufficient conditions for the nonlinear case are investigated with the help of the Banach contraction mapping theorem. Finally, we add some examples to elaborate on our work.

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Controllability and Observability of Fractional Linear Systems with Two Different Orders

Cited by 12 publications

References 19 publications

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

Network Intervention, a Method to Address Complex Therapeutic Strategies

Controllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical System

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