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This work deals with the robust D-stability test of linear time-invariant ( LTI ) general fractional order control systems in a closed loop where the system and - or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on... 

This paper investigates the robust D -stability test of LTI fractional order interval systems (FOISes). The D stability includes the performance of an LTI system in addition to stability. The coefficients of the system transfer function are uncertain parameters that each adopts a value in a real interval. Firstly, the concept of the value set is extended to the FOISes, and a necessary and sufficient condition is presented to study the robust D-stability of FOISes. Secondly, the value set of the FOISes is obtained analytically, and based on it a robust D- stability testing function is introduced to check the presented condition. The results obtained are applicable to systems of both... 

In Ref. [1], it has been claimed that the value set of a fractional order interval plant, having one uncertain time delay is a polygon. This note illustrates that this claim is not true, and in fact the value set has a nonconvex shape. Therefore, Theorem 3.1 and the stabilization algorithm presented in the reference to design a PIλDμ controller, are not true. © 2018 Elsevier B.V  

This paper presents fractional order multi-input multi-output (MIMO) controllers for the robust performance of airplane longitudinal motion. A novel necessary and sufficient criterion is offered by using the value set concept to analyze the robust performance of fractional order MIMO uncertain systems based on the location of the characteristic equation roots. The criterion is applicable to all linear time-invariant systems of commensurate and incommensurate orders with complex coefficients. The obtained results are applied to an uncertain linear model of a business airplane to improve the robust performance of its longitudinal motion by decentralized MIMO output feedback and MIMO state... 

This study focuses on the robust D-stability analysis of fractional order interval systems (FOISes). The concept of interval means that the coefficients of the systems transfer functions are uncertain parameters that each adopts a value in a real interval. Initially, some new bounds on the poles of the FOISes are produced so that they reduce the computational burden in the case of the θ-stability. Then, the concept of the value set is extended to analyse the robust D-stability of the FOISes, and a new necessary and sufficient condition is presented. The value set of the FOISes is obtained analytically, and based on it an auxiliary function is introduced to check the condition. The obtained... 

This article focuses on the robust D-stabilization analysis of fractional-order control systems where each of the system and the controller may be of fractional order. The coefficients of the system are considered as complex linear functions of interval uncertain parameters, so this article deals with fractional-order polytopic systems. First, a necessary and sufficient condition is introduced for the robust D-stabilization of the closed-loop control system based on the zero exclusion condition and the value set concept. Then, the geometric pattern of the value set of the characteristic polynomial is obtained analytically using the exposed vertices. Second, a function is presented to check... 

This paper investigates the robust D-stability criterion of fractional order systems with parametric uncertainties. Uncertainties are considered in the both coefficients and orders of the fractional order systems. To this end, some bounds on the roots of fractional order polynomials are obtained, helping to examine the robust D-stability criterion. Then, by using the zero exclusion principle a necessary and sufficient criterion to check the robust D-stability is presented. The obtained results can be applied to fractional order systems of both commensurate and incommensurate orders. One numerical example is given to verify the results. © 2018 AACC  

This paper investigates the robust stability analysis of fractional-order interval systems with multiple time delays, including retarded and neutral systems. A bound on the poles of fractional-order interval systems of retarded and neutral type is obtained. Then, the concept of the value set and zero exclusion principle is extended to these systems, and a necessary and sufficient condition is produced for checking the robust stability of them. The value set of the characteristic equation of the systems is obtained analytically and, based on it, an auxiliary function is introduced to check the zero exclusion principle. Finally, two numerical examples are given to illustrate the effectiveness... 

This study focuses on the robust D-stability analysis of fractional order interval systems (FOISes). The concept of interval means that the coefficients of the systems transfer functions are uncertain parameters that each adopts a value in a real interval. Initially, some new bounds on the poles of the FOISes are produced so that they reduce the computational burden in the case of the θ-stability. Then, the concept of the value set is extended to analyse the robust D-stability of the FOISes, and a new necessary and sufficient condition is presented. The value set of the FOISes is obtained analytically, and based on it an auxiliary function is introduced to check the condition. The obtained... 

This article focuses on the robust D-stabilization analysis of fractional-order control systems where each of the system and the controller may be of fractional order. The coefficients of the system are considered as complex linear functions of interval uncertain parameters, so this article deals with fractional-order polytopic systems. First, a necessary and sufficient condition is introduced for the robust D-stabilization of the closed-loop control system based on the zero exclusion condition and the value set concept. Then, the geometric pattern of the value set of the characteristic polynomial is obtained analytically using the exposed vertices. Second, a function is presented to check... 

A new method of integrated guidance and control for homing missiles with actuator fault against manoeuvring targets is proposed. Model of the integrated guidance and control system in the pitch plane with actuator fault and some uncertainty is developed. A control law using combination of adaptive backstepping and sliding mode approaches is designed to achieve interception in the presence of bounded uncertainties and actuator fault. Simulation results show that new approach has better performance than adaptive backstepping and has good performance in the presence of actuator fault  

Secure routing is a major key to service maintenance in ad hoc networks. Ad hoc nature exposes the network to several types of node misbehavior or attacks. As a result of the resource limitations in such networks nodes may have a tendency to behave selfishly. Selfish behavior can have drastic impacts on network performance. We have proposed a Misbehavior-Tolerant Multipath Routing protocol (MTMR) which detects and punishes all types of misbehavior such as selfish behavior, wormhole, sinkhole and grey-hole attacks. The protocol utilizes a proactive approach to enforce cooperation. In addition, it uses a novel data redirection method to mitigate the impact of node misbehavior on network... 

This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation?
Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data.
The book provides an overview of methods that have been developed for the analysis of... 

Consider the parameter Λ(G) = |E(G)| - |V(G)|(k - 1) + (k2) for a k-chromatic graph G, on the set of vertices V(G) and with the set of edges E(G). It is known that Λ(G)≥0 for any k-chromatic uniquely vertex-colourable graph G (k-UCG), and, S.J. Xu has conjectured that for any k-UCG, G, Λ(G) = 0 implies that cl(G) = k; in which cl(G) is the clique number of G. In this paper, first, we introduce the concept of the core of a k-UCG as an induced subgraph without any colour-class of size one, and without any vertex of degree k - 1. Considering (k, n)-cores as k-UCGs on n vertices, we show that edge-minimal (k, 2k)-cores do not exist when k ≥ 3, which shows that for any edge-minimal k-UCG on 2k...