2020 (vol. 30) - Number 4

*A.B. Malinowska, R. Kamocki, R. Almeida, T. Odzijewicz:*

On the existence of optimal consensus control for the fractional Cucker--Smale model

*R. Grymin, W. Bożejko, J. Pempera, M. Wodecki, Z. Chaczko:*

Algorithm for solving the Discrete-Continuous Inspection Problem

*T. Kaczorek, A. Ruszewski:*

Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

*R. Arora, K. Gupta:*

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

*P. Nowak, J. Czeczot, P. Grelewicz:*

Tuning rules for industrial use of the second-order Reduced Active Disturbance Rejection Controller

*M.I. Gomoyunov:*

Optimal control problems with a fixed terminal time in linear fractional-order systems

*Muhafzan, A. Nazra, L. Yulianti, Zulakmal, R. Revina:*

On LQ optimization problem subject to fractional order irregular singular systems

*M. Blizorukova, V. Maksimov:*

On one algorithm for reconstruction of an disturbance in a linear system of ordinary differential equations

ACS Abstract:

**2018 (Volume 28)**

Number 4

A new method for computation of positive realizations of fractional linear continuous-time systems

T. Kaczorek(Bialystok University of Technology, Poland) |

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.

**keywords:** determination, positive, realization, transfer matrix, linear, continuous-time, fractional, system

Development of dual hesitant fuzzy prioritized operators based on Einstein operations with their application to multi-criteria group decision making

A. Biswas(University of Kalyani, India) | A. Sarkar(Heramba Chandra College, Kolkata, India) |

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.

**keywords:** multi-criteria group decision-making, aggregation operator, dual hesitant fuzzy numbers, Einstein operations, prioritized weighted averaging operator, prioritized weighted geometric operator

Some q-orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making

L. Li, R. Zhang, J. Wang, X. Shang(Beijing Jiaotong University, China) |

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-ROLWHM) 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.

**keywords:** q-rung orthopair fuzzy set, q-rung orthopair linguistic set, Heronian mean, q-rung orthopair linguistic Heronian mean, multi-attribute group decision making

Lyapunov matrices approach to the parametric optimization of a system with two delays and a PD controller

J. Duda(AGH University of Science and Technology, Krakow, Poland) |

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.

**keywords:** neutral system, Lyapunov matrix, Lyapunov functional

Ideal observability for bilinear discrete-time systems with and without delays in observation

M. Lhous, M. Rachik, El M. Magri(Hassan II University of Casablanca, Morocco) |

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.

**keywords:** bilinear systems, Hilbert spaces, ideal observability, observability subspace, delayed observation

Variation of constant formulas for fractional difference equations

P.T. Anh(Le Quy Don Technical University, Vietnam) | A. Babiarz, A. Czornik, M. Niezabitowski(Silesian University of Technology, Poland) |

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.

**keywords:** fractional difference equation, variation of constants, separation of solutions

A comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems

K. Bingi, R. Ibrahim, M. Noh Karsiti, S. Miya Hassan(Universiti Teknologi PETRONAS, Malaysia) | V. Rajah Harindran(PETRONAS Group Technical Solutions, Malaysia) |

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.

**keywords:** fractional order controller, set-point weighting, 2DOF PID, process control, unstable systems

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