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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 study deals with the subject of robust bounded-input bounded-output (BIBO)-stability of a family of fractional order interval systems. Employing the idea of'robust stability testing function'and extending it to the case of intended systems, a simple graphical procedure for checking the robust BIBO-stability applicable to both commensurate and incommensurate orders is developed. Moreover, a Kharitonov-like theorem is provided that presents necessary and sufficient conditions for checking the mentioned stability of the fractional order interval systems with commensurate order α belonging to [1,2), but only sufficient conditions for commensurate order α in interval (0,1). Besides, lower... 

BIBO stability of linear time-invariant (LTI) distributed order dynamic systems with non-negative weight functions is investigated in this paper by using Lagrange inversion theorem. New sufficient conditions of stability/instability are presented for these systems accordingly. These algebraically simple conditions are relatively tight and their conservatism is adjustable. © 2018 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd  

BIBO stability of linear time-invariant (LTI) distributed order dynamic systems with non-negative weight functions is investigated in this paper by using Lagrange inversion theorem. New sufficient conditions of stability/instability are presented for these systems accordingly. These algebraically simple conditions are relatively tight and their conservatism is adjustable. © 2018 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd  

This paper mainly focuses on some behaviours of the bounded input-bounded output (BIBO) stability boundary in the linear distributed-order system (LDOS). Finding an association between changes of weight functions of LDOS and variation of its BIBO stability boundary is the other aim of this paper. To achieve these goals, the tangential lines of the BIBO stability boundary for the extremely high and low frequencies are founded in the first step. Then, the additive identity and the multiplicative identity for the weight function maintaining the stability boundary intact are determined. In addition, it is proved that multiplying a set of multiplication factors in the form of polynomials to the... 

This paper considers a closed-loop system consisting of a fractional/integer order system and a fractional PID controller. Assuming that the uncertain coefficients of the fractional PID controller lie in some known intervals independently (i.e. that controller is a member of an interval family), the paper presents some easy to use theorems to investigate the robust bounded-input bounded-output stability of the resultant closed-loop system. Moreover, a finite frequency bound required in drawing the related graphs has also been provided. Finally, some numerical examples are presented to illustrate the results  

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  

In this paper, the computation of robustness margin for linear time invariant fractional order systems is studied. For the definition of robustness margin, we employ the one introduced for polynomials (i.e. integer order) and extend it to fractional order functions. Using the well known concept of the value set and knowing its shape for the intended functions, this paper presents an easy way to obtain the robustness margin for fractional order systems. To illustrate the results, a numerical example is provided  

This paper deals with the stability problem in LTI fractional order systems having fractional orders between 1 and 1.5. Some sufficient algebraic conditions to guarantee the BIBO stability in such systems are obtained. The obtained conditions directly depend on the coefficients of the system equations, and consequently using them is easier than the use of conditions constructed based on solving the characteristic equation of the system. Some illustrations are presented to show the applicability of the obtained conditions. For example, it is shown that these conditions may be useful in stabilization of unstable fractional order systems or in taming fractional order chaotic systems  

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  

This paper presents a numerical algorithm for BIBO stability testing of a certain class of the so-called fractional-delay systems. The characteristic function of the systems under consideration is a multi-valued function of the Laplace variable s which is defined on a Riemann surface with finite number of Riemann sheets where the origin is a branch point. The stability analysis of such systems is not straightforward because there is no universally applicable analytical method to find the roots of the characteristic equation on the right half-plane of the first Riemann sheet. The proposed method is based on the Rouche's theorem which provides the number of the zeros of a given function in a...