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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 paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type. In the proposed method, first, by mapping the principal sheet of the Riemann surface and a pseudo-delay transformation, an auxiliary polynomial is generated. Then, this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis. The properties of the root path close to these roots are used to identify intervals of delay values, in which the system is stable. The obtained results are illustrated via some numerical examples  

This study presents a new approach to decompose singular time-delay systems (STDSs) in a way that they can be transformable to normal time-delay systems (TDSs) with a lower order. Necessary and sufficient conditions are provided to determine which STDSs can be transformed to TDSs. Also, a stabilisation method is provided to stabilise the system, while the time delay in the system can belong to several distinct intervals or even everywhere. The proposed method is non-fragile towards controller parameters. This method also reveals one of the many applicable situations of the proposed decomposition. The effectiveness of the proposed method is illustrated through some examples. © 2018 The... 

This paper studies fractional-order systems of retarded type with two independent delays, and determines the stability regions in spaces of delays. In this approach, an auxiliary polynomial is employed to calculate all purely imaginary roots of the characteristic equation of the system on the imaginary axis. Since roots of the characteristic equation are continuous with respect to delays, these purely imaginary roots determine the stability regions in delay space. Also, the necessary and sufficient condition for stability independent of delays is developed for the systems. Furthermore, a simple inequality constraint is established to obtain pure imaginary poles of the scalar systems.... 

In this work, a novel method is proposed to study the BIBO stability of a fractional delay system. The characteristic equation of a fractional delay system with some transcendental terms has infinitely many roots. Applying D-subdivision method and the Rekasius substitution divide one-dimensional parametric space of the time delay to infinite intervals with finite unstable roots. The number of unstable roots in each interval is calculated with the definition of root tendency on the boundary of each interval. Two illustrative examples are presented to confirm the proposed method results  

The time delay equations are frequently used to model real systems since they can describe the after-effect phenomenon. It is usually difficult to analyze the properties of time delay systems. Thus it would be beneficial to make the systems as simple as possible. For this purpose, the decomposition of the systems into some separate or cascaded sub-systems with smaller dimension is introduced as the solution of the mentioned complex task. The decomposition of the time delay systems with one delay is directly related to simultaneous similarity of two matrices. In this regard, necessary and sufficient conditions are derived for the existence of a common similar block diagonal or triangular form... 

Control of unstable non-minimum-phase delayed stochastic processes is a challenging problem. In this work based on the Diophantine equation and using pole-placement technique, a discrete control scheme for such processes has been proposed. Robust stability of the suggested control structure has been shown. Advantages of the proposed scheme over the existing algorithms have been shown through computer simulations. It has been shown that performance of the proposed scheme for handling model mismatch and colored noise is superior to the previous work proposed in the literature  

The problem of tuning a two-parameter controller has been formulated as finding the centroid of the admissible region specified by the set of constraints that the controller should satisfy. The constraints can be as general as the closed-loop system stability or they may include several requirements on various stability, sensitivity, or performance measures. The design of stabilizing proportional-derivative (PD) controllers using the centroid of the stability region in the controller parameter space is considered as a case study. To this end, analytical formulas are derived to describe the stability boundaries of a class of integrating time delay systems, the stability region of which has a... 

This study deals with proposing a Lyapunov-based technique for stability analysis of fractional order time-delay systems. The proposed technique is constructed on the basis of modifying the convex part of a class of Lyapunov-Krasovskii functionals commonly used in stability analysis of integer order time-delay systems. As a consequence for this achievement, it is revealed that the Lyapunov-Krasovskii-based stability conditions in integer order time-delay systems can result in stability of their fractional order counterparts defined based on Caputo/Riemann-Liouville derivative operators with orders in the range (0,1). The applicability of the study results is shown through three different... 

During power system restoration, it is necessary to check the phase angle between two buses before closing circuit breakers to connect a line between them. These angles may occur across a tie line between two systems or between two connected subsystems within a system. In case of large Standing Phase Angle (SPA) difference the synchrocheck relay does not allow closing of the breaker for this line. Therefore, this excessive SPA has to be reduced before attempting to connect the line. In this paper a new and fast method for reducing SPA is presented. For this purpose, the standing phase angle difference between two specific buses is represented in terms of sensitivity factors associated with... 

This paper studies fractional-order systems of retarded type with two independent delays, and determines the stability regions in spaces of delays. In this approach, an auxiliary polynomial is employed to calculate all purely imaginary roots of the characteristic equation of the system on the imaginary axis. Since roots of the characteristic equation are continuous with respect to delays, these purely imaginary roots determine the stability regions in delay space. Also, the necessary and sufficient condition for stability independent of delays is developed for the systems. Furthermore, a simple inequality constraint is established to obtain pure imaginary poles of the scalar systems.... 

In this paper a new approach is developed to stabilize descriptor systems with time-delay, while time-delay can belong to a given interval. This approach takes the advantages of system's singularity to simplify the model and uses the so-called Rekasius substitution to compute the controller parameters in a way that the asymptotic stability of the closed-loop system in the given interval of the delay can be guaranteed. Finally, a numerical example is provided to evaluate the proposed method's effectiveness. © 2017 IEEE  

A fractional order PID controller is designed to stabilize fractional delay systems with commensurate orders and multiple commensurate delays, where the time delays in the system may belong to several distinct intervals. Moreover, the controller parameters should belong to given intervals. In order to stabilize the system, the D-subdivision method is employed to choose the stabilizing set of the controller parameters from their available values. Furthermore, the nearest values of the obtained stabilizing set to their mean values are selected as the controller parameters so that a non-fragile controller is concluded. Two numerical examples evaluate the proposed control design method  

In this note, bounded-input bounded-output (BIBO)-stability of a large class of neutral type fractional delay systems is investigated. Necessary and sufficient conditions of BIBO-stability are presented for the intended class of systems (the sufficient conditions have been provided for a more general case in the previous studies). Two lemmas are provided for checking a prerequisite imposed on the considered class of systems. Finally, two numerical examples are given to illustrate the obtained results  

This paper deals with the analysis of robust BIBO-stability of LTI fractional order delay systems in the presence of real parametric uncertainties. Two large classes of these systems, namely retarded and neutral types, are considered. Two theorems are given to check the robust BIBO-stability of these two families of fractional order systems. One of these theorems provides necessary and sufficient conditions for the case of retarded type and another one presents only sufficient conditions for the case of neutral type. Furthermore, upper and lower bounds (cutoff frequencies) are provided for drawing the value sets. To illustrate the results, two numerical examples are presented  

The bounded-input bounded-output stability of fractional delay systems of neutral type is investigated in this study. The proposed method calculates the number of unstable poles of the system for each delay value. All time-delay intervals in time-delay space where system is stable are precisely determined. The stability of systems with not only indefinitely large values of time-delay, but also with multiple poles on the imaginary axis has been studied. The proposed method is employed for investigating the stability of a fractional delay system when its fractional orders approach to the integer numbers or zero. It is proved that simple case of neutral types and time-delay systems have the...