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Lyapunov matrices approach to the parametric optimization of a system with two delay sand a PD-controller

Józef Duda
Archives of Control Sciences | 2018 | vol. 28 | No 4 | 585-600 | DOI: 10.24425/acs.2018.125484
Keywords neutral system Lyapunov matrix Lyapunov functional
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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

The parametric optimization of a system with two delays and a PI controller

Jozef Duda
Archives of Control Sciences | 2019 | vol. 29 | No 4 | 667-686 | DOI: 10.24425/acs.2019.131231
Keywords time-delay system Lyapunov matrix Lyapunov functional
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Abstract

In the paper a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two commensurate delays and a PI-controller is presented. The value of integral quadratic performance index is equal to the value of the Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper is presented the example of a scalar system with two delays and a PI controller.

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Authors and Affiliations

Jozef Duda

Global rational stabilization of a class of nonlinear time-delay systems

Nadhem Echi Boulbaba Ghanmi
Archives of Control Sciences | 2019 | vol. 29 | No 2 | 259–278 | DOI: 10.24425/acs.2019.129381
Keywords rational stability delay system nonlinear observer Lyapunov functional
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Abstract

The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics.

Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points.

Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.

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Authors and Affiliations

Nadhem Echi
Boulbaba Ghanmi

Discrete-time Takagi-Sugeno singular systems with unmeasurable decision variables: state and fault fuzzy observer design

Khaoula Aitdaraou Mohamed Essabre Abdellatif El Assoudi El Hassane El Yaagoubi
Archives of Control Sciences | 2023 | vol. 33 | No 2 | 321-328 | DOI: 10.24425/acs.2023.146278
Keywords observer design unmeasurable decision variable SVD approach Lyapunov function LMIs
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Abstract

The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach.
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Authors and Affiliations

Khaoula Aitdaraou
1 2
Mohamed Essabre
3
Abdellatif El Assoudi
1 2
El Hassane El Yaagoubi
1 2
  1. Laboratory of High Energy Physics and Condensed Matter, Faculty of Science, Hassan II University of Casablanca, B.P 5366, Maarif Casablanca, Morocco
  2. ECPI, Department of Electrical Engineering, ENSEM Hassan II University of Casablanca, B.P 8118, Oasis Casablanca, Morocco
  3. Laboratory of Materials, Energy and Control Systems, Faculty of Sciences and Technologies Mohammedia, Hassan II University of Casablanca, Morocco

On the region of attraction of dynamical systems: Application to Lorenz equations

M.A. Hammami N.H. Rettab
Archives of Control Sciences | 2020 | vol. 30 | No 3 | 389-409 | DOI: 10.24425/acs.2020.134671
Keywords nonlinear dynamical systems Lyapunov function Basin of attraction Lorenz equations
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Abstract

Many nonlinear dynamical systems can present a challenge for the stability analysis in particular the estimation of the region of attraction of an equilibrium point. The usual method is based on Lyapunov techniques. For the validity of the analysis it should be supposed that the initial conditions lie in the domain of attraction. In this paper, we investigate such problem for a class of dynamical systems where the origin is not necessarily an equilibrium point. In this case, a small compact neighborhood of the origin can be estimated as an attractor for the system. We give a method to estimate the basin of attraction based on the construction of a suitable Lyapunov function. Furthermore, an application to Lorenz system is given to verify the effectiveness of the proposed method.

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Authors and Affiliations

M.A. Hammami
N.H. Rettab

Exponential stability of impulsive delayed nonlinear hybrid differential systems

Qianqian Jia Chaoying Xia
Archives of Electrical Engineering | 2019 | vol. 68 | No 3 | 553-564 | DOI: 10.24425/aee.2019.129341
Keywords impulsive delayed nonlinear hybrid systems global exponential Lyapunov function Razumikhin technique
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Abstract

In recent years, with the rapid development of digital components, digital electronic computers, especially microprocessors, digital controllers have replaced analog controllers on many occasions. The application of digital controller makes the performance analysis of impulsive system more and more important. This paper considers global exponential stability (GES) of impulsive delayed nonlinear hybrid differential systems (IDNHDS).Through the application of the Lyapunov method and the Razumikhin technique, a series of uncomplicated and useful guiding principles have been obtained. The results of a numerical simulation are presented to demonstrate that the method is correct and effective.

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Authors and Affiliations

Qianqian Jia
Chaoying Xia

The Stability Interval of the Set of Linear System

Talgat Mazakov Waldemar Wójcik Sholpan Jomartova Nurgul Karymsakova Gulzat Ziyatbekova Aisulu Tursynbai
International Journal of Electronics and Telecommunications | 2021 | vol. 67 | No 2 | 155-161 | DOI: 10.24425/ijet.2021.135958
Keywords automatic control system stability matrix minor characteristic polynomial Hurwitz criterion Lienard-Shipard criterion of interval mathematics Lyapunov function
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Abstract

The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and Lienard- Shipar interval criteria. Krylov, Leverier, and Leverier- Danilevsky algorithms are implemented for automated construction and analysis of the interval characteristic polynomial. The interval mathematics library was used while developing the software. The stability of the dynamic system described by linear ordinary differential equations is determined and based on the properties of the eigenvalues of the interval characteristic polynomial. On the basis of numerical calculations, the authors compare several methods of constructing the characteristic polynomial. The developed software that implements the introduced interval arithmetic operations can be used in the study of dynamic properties of automatic control systems, energy, economic and other non-linear systems.
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Bibliography

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Authors and Affiliations

Talgat Mazakov
1
Waldemar Wójcik
2
Sholpan Jomartova
1
Nurgul Karymsakova
3
Gulzat Ziyatbekova
1
Aisulu Tursynbai
3
  1. Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Almaty, Kazakhstan
  2. Lublin Technical University, Poland
  3. Al-Farabi Kazakh National University, Almaty, Kazakhstan

Hybrid synchronization and parameter estimation of a complex chaotic network of permanent magnet synchronous motors using adaptive integral sliding mode control

Nazam Siddique Fazal U. Rehman
Bulletin of the Polish Academy of Sciences Technical Sciences | 2021 | 69 | 3 | e137056 | DOI: 10.24425/bpasts.2021.137056
Keywords chaotic systems hybrid synchronization (HS) complex chaotic permanent magnet synchronous motor adaptive integral sliding mode control (ISMC) Lyapunov function
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Abstract

The synchronisation of a complex chaotic network of permanent magnet synchronous motor systems has increasing practical importance in the field of electrical engineering. This article presents the control design method for the hybrid synchronization and parameter estimation of ring-connected complex chaotic network of permanent magnet synchronous motor systems. The design of the desired control law is a challenging task for control engineers due to parametric uncertainties and chaotic responses to some specific parameter values. Controllers are designed based on the adaptive integral sliding mode control to ensure hybrid synchronization and estimation of uncertain terms. To apply the adaptive ISMC, firstly the error system is converted to a unique system consisting of a nominal part along with the unknown terms which are computed adaptively. The stabilizing controller incorporating nominal control and compensator control is designed for the error system. The compensator controller, as well as the adopted laws, are designed to get the first derivative of the Lyapunov equation strictly negative. To give an illustration, the proposed technique is applied to 4-coupled motor systems yielding the convergence of error dynamics to zero, estimation of uncertain parameters, and hybrid synchronization of system states. The usefulness of the proposed method has also been tested through computer simulations and found to be valid.
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Authors and Affiliations

Nazam Siddique
1
ORCID: ORCID
Fazal U. Rehman
1
  1. Capital University of Science and Technology, Islamabad Expressway, Kahuta Road, Zone-V Islamabad, Pakistan

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