Applied sciences

Archives of Control Sciences

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Archives of Control Sciences | 2018 | vol. 28 | No 4 |

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Abstract

A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

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Authors and Affiliations

Tadeusz Kaczorek
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Abstract

The purpose of this article is to develop a multicriteria group decision making (MCGDM) method in dual hesitant fuzzy (DHF) environment by evaluating the weights of the decision makers from the decision matrices using two newly defined prioritized aggregation operators based on score function to remove the inconsistencies in choosing the best alternative. Prioritized weighted averaging operator and prioritized weighted geometric operator based on Einstein operations are described first for aggregating DHF information. Some of their desirable properties are also investigated in details. A method for finding the rank of alternatives in MCGDM problems with DHF information based on priority levels of decision makers is developed. An illustrative example concerning MCGDM problem is considered to establish the application potentiality of the proposed approach. The method is efficient enough to solve different real life MCGDM problems having DHF information.

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Authors and Affiliations

Animesh Biswas
Arun Sarkar
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Abstract

The recently proposed q-rung orthopair fuzzy set (q-ROFS) characterized by a membership degree and a non-membership degree is powerful tool for handling uncertainty and vagueness. This paper proposes the concept of q-rung orthopair linguistic set (q-ROLS) by combining the linguistic term sets with q-ROFSs. Thereafter, we investigate multi-attribute group decision making (MAGDM) with q-rung orthopair linguistic information. To aggregate q-rung orthopair linguistic numbers ( q-ROLNs), we extend the Heronian mean (HM) to q-ROLSs and propose a family of q-rung orthopair linguistic Heronian mean operators, such as the q-rung orthopair linguistic Heronian mean (q-ROLHM) operator, the q-rung orthopair linguistic weighted Heronian mean (q-ROLWHM) operator, the q-rung orthopair linguistic geometric Heronian mean (q-ROLGHM) operator and the q-rung orthopair linguistic weighted geometric Heronian mean (q-ROLWGHM) operator. Some desirable properties and special cases of the proposed operators are discussed. Further, we develop a novel approach to MAGDM within q-rung orthopair linguistic context based on the proposed operators. A numerical instance is provided to demonstrate the effectiveness and superiorities of the proposed method.

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Authors and Affiliations

Li Li
Runtong Zhang
Jun Wang
Xiaopu Shang
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Abstract

In the paper the parametric optimization problem for a linear system with two delays and a PD-controller is presented. In the parametric optimization problem the quadratic performance index is considered. The value of the quadratic index of quality is calculated due to the Lyapunov functional and is equal to the value of that functional for the initial function of the neutral system with two delays. The Lyapunov functional is determined by means of the Lyapunov matrix.

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Authors and Affiliations

Józef Duda
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Abstract

An ideal observability subspace expression is stated for bilinear abstract system with bounded operator in Hilbert spaces. The case of finite dimentional space is also treated. However, it’s noticed that the state ideal observability can never be fulfilled within an infinite dimensional phase space in the case of scalar output. The case of bilinear discrete-time system with delays in observation is also described. To illustrate this work some examples are presented.

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Authors and Affiliations

Mustapha Lhous
Mostafa Rachik
El Mostafa Magri
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Abstract

In this paper, we establish variation of constant formulas for both Caputo and Riemann- Liouville fractional difference equations. The main technique is the Z -transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.

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Authors and Affiliations

Pham The Anh
Artur Babiarz
Adam Czornik
Michał Niezabitowski
Stefan Siegmund
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Abstract

The proportional-integral-derivative (PID) controllers have experienced series of structural modifications and improvements. Example of such modifications are set-point weighting and fractional ordering. While the former is to achieve two-degree-of-freedom (2DOF) ability of set-point tracking and disturbance rejection, the latter is to ensure smooth control action. Therefore, this paper reviews various forms of PID controllers and provides a comparative analysis of 2DOF PID and 2DOF fractional order PID (FOPID) controllers. The paper also discusses the conversion of one PID form to another. For the comparative analysis of the various controllers, a class of unstable systems are considered. Simulation result shows that in most cases the conversion from one form to another does not significantly affect the performance of the system. It is also observed that the 2DOF controllers (2DOF PID and 2DOF FOPID) improved significantly the performance of the ordinary PID controllers.

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Authors and Affiliations

Kishore Bingi
Rosdiazli Ibrahim
Mohd Noh Karsiti
Sabo Miya Hassan
Vivekananda Rajah Harindran

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