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Rational approximations in the simulation and implementation of fractional-order dynamics: A descriptor system approach
, Article Automatica ; Volume 46, Issue 1 , 2010 , Pages 94-100 ; 00051098 (ISSN) ; Haeri, M ; Sharif University of Technology
2010
Abstract
This paper deals with issues related to the use of rational approximations in the simulation of fractional-order systems and practical implementations of fractional-order dynamics and controllers. Based on the mathematical formulation of the problem, a descriptor model is found to describe the rational approximating model. This model is analyzed and compared with the original fractional-order system under the aspects which are important in their simulation and implementation. From the results achieved, one can determine in what applications the use of rational approximations would be unproblematic and in what applications it would lead to fallacious results. In order to clarify this point,...
Stability analysis of descriptor systems with multiple commensurate time-delays
, Article Journal of the Franklin Institute ; Volume 356, Issue 15 , 2019 , Pages 8690-8705 ; 00160032 (ISSN) ; Haeri, M ; Sharif University of Technology
Elsevier Ltd
2019
Abstract
A new method is proposed to analyze stability of descriptor systems with multiple commensurate time-delays. In this method, purely imaginary roots of the system are calculated, asymptotic behavior of root path at these roots is studied, and unstable regions of the system in the space of delays are determined. Moreover, the number of roots in each unstable region is calculated. Also necessary and sufficient conditions for τ-stabilizability of these systems are presented. Examples are provided to illustrate the effectiveness and validity of the proposed method. © 2019 The Franklin Institute
Asymptotic stability of linear descriptor systems with time-delay by designing delay margin
, Article 5th International Conference on Control, Instrumentation, and Automation, ICCIA 2017 ; Volume 2018-January , 2018 , Pages 23-29 ; 9781538621349 (ISBN) ; Haeri, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018
Abstract
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
Stability Analysis and Stabilization of Descriptor Systems with Time-Delay
, M.Sc. Thesis Sharif University of Technology ; Haeri, Mohammad (Supervisor)
Abstract
In this thesis, the general form of descriptor linear systems with time-delay is studied. First, an approach is presented to analyze the stability of descriptor linear systems with commensurate time-delay. Through this approach, not only stable and unstable regions of the system can be determined, but also the number of unstable roots in each unstable region can be calculated. Additionally, a decomposition approach is proposed, which transforms the descriptor systems with time-delay to normal time-delay systems with a lower order. As a result, a large number of methods which are only available for normal systems with time-delay can be utilized for descriptor systems with time-delay. Also,...