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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 letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using... 

The performance of hapticdevicesisevaluatedbasedontheconceptoftransparency, whiletheirstabilityhasprevalentlybeenevaluatedbasedonthepassivitycriterion. Duetotheconservativenessofpassivity, itappearsasanobstacletoimprovingtransparency.Inthepresentpaper, passivityissuggestedtobereplacedbythecomplementarystabilitycriterionwhichaccoun tsfortherobuststabilityoftheinteractioninthepresnceofuncertainuserhanddynamics. Inthisrespect, analgorithmisproposedwhichguaranteestransparencyofthehapticdeviceinastablemanne r.Assumingthatthedynamicsofthedeviceisknown, acertaincompensatorystructureisassigned. Thisspecialstructureguaranteestransparencyofthedevicebycompensatingforthedynami... 

This study investigates the dynamic participation of wind power plants (WPPs) in the automatic generation control (AGC) task. The pre-specified model of wind farm in the AGC studies has been used. It is shown that operating of WPPs at the command mode results in a significant improvement in the frequency behaviour of power system due to their faster response. However, the WPPs may change their operation mode from the command mode to the maximum power point mode according to the wind speed conditions and load variations. This reduces the improvement in the frequency response. In this condition, the shortage in the wind power should be compensated by the conventional units. Thus, the share of... 

Robust stability analysis of multiorder fractional linear time-invariant systems is studied in this paper. In the present study, first, conservative stability boundaries with respect to the eigenvalues of a dynamic matrix for this kind of systems are found by using Young and Jensen inequalities. Then, considering uncertainty on the dynamic matrix, fractional orders, and fractional derivative coefficients, some sufficient conditions are derived for the stability analysis of uncertain multiorder fractional systems. Numerical examples are presented to confirm the obtained analytical results. Copyright © 2017 John Wiley & Sons, Ltd  

In this paper, a new approach is suggested to investigate stability in a family of fractional order linear time invariant systems with order between 1 and 2. The proposed method relies on finding a linear ordinary system that possesses the same stability property as the fractional order system. In this way, instead of performing the stability analysis on the fractional order systems, the analysis is converted into the domain of ordinary systems which is well established and well understood. As a useful consequence, we have extended two general tests for robust stability check of ordinary systems to fractional order systems. © 2008 IMACS  

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 studies the robust stability of the fractional-order (FO) LTI systems with polytopic uncertainty. Generally, the characteristic polynomial of the system dynamic matrix is not an affine function of the uncertain parameters. Consequently, the robust stability of the uncertain system cannot be evaluated by well-known approaches including LMIs or exposed edges theorem. Here, an over-parameterization technique is developed to convert the main characteristic polynomial into a set of local over-parameterized characteristic polynomials (LOPCPs). It is proved that the robust stability of LOPCPs implies the robust stability of the uncertain system. Then, an algorithm is proposed to explore... 

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... 

the parallel form in adaptive HR filtering is an efficient realization that provides robust stability monitoring with less complexity than that of the direct form. This paper presents an implementation of two line parallel structure employing a real orthogonal transform and real coefficients second-order section as sub filters on FPGA. Architecture that is implemented is in pipeline fashion and it is independent from its building blocks and they may have its own implementation or in other system numbering. In the last section, we compared throughput of our architecture with a Ti DSP (TMS320C3x/4x), the results show that this architecture works better than the DSP  

H∞ controller order reduction with stability and performance preservation pose unique challenges to designers. In the paper, an approach for controller order reduction based on minimization of the rank of a matrix variable, subject to linear matrix inequality constraints, is presented. In this approach, the rank of a residue matrix of a high-order controller subject to the error between the loop gain of the closed-loop nominal system and the loop gain of the closed-loop system with the reduced order controller is minimized. However, since solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with the nuclear-norm that can be reduced to a... 

An application of the multiple models adaptive control based on switching and tuning to a flexible transmission system will be presented. This approach has been considered in order to assure high control performance in the presence of large load variation on the system. The advantages of the multiple models adaptive control system with respect to the classical adaptive control will be illustrated via the experimental results. It will also be shown that the robustness of the adaptive control system can be improved with the appropriate shaping of a sensitivity function. The use of a recently developed parameter estimation algorithm based on the minimization of the closed-loop output error in... 

In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional order α is a known constant belonging to 0 < α < 1. Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and... 

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... 

Performance of a haptic device is evaluated based on the concept of transparency. Stability of a haptic device prevalently has been evaluated based on the passivity criterion. Due to conservativeness of passivity, it appears as an obstacle to improve transparency. In this paper, passivity is suggested to be replaced by the complementary stability criterion which accounts for the robust stability of the interaction in the presence of uncertain user hand dynamics. In this respect, an algorithm is proposed which guarantees transparency of the haptic device in a stable manner. Assuming that the dynamics of the device is known, a certain compensatory structure is assigned. This special structure... 

In this paper the impulsive synchronization of general continuous chaotic and hyperchaotic systems is investigated. The robust stability of the synchronization method is examined in the presence of uncertainties both on linear and nonlinear parts of the system dynamics and the channel noise. Conditions on the impulse distances are derived for different cases. Numerical simulations are presented to show the effectiveness of the method. © 2007 Elsevier B.V. All rights reserved  

This article uses gap metric method to design a multi-model controller for nonlinear systems. In order to decompose the nonlinear system into a reduced nominal local models bank as much as possible, and assure the closed-loop robust stability and performance, the decomposition and designing of local controllers are integrated. To this end, robust stability, performance, and gap metric are incorporated to build a binary distance matrix that supports defining the driving and dependence powers for each local model. Then a best–worst analysis is employed considering the driving and dependence powers to find out the nominal local models. The proposed approach screens the value of all local models...