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Number of results: 23
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Abstract

The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical examples and an example of positive electrical circuit.

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Authors and Affiliations

Tadeusz Kaczorek
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Abstract

A novel current-inversion type negative impedance converter (CNIC) is presented. It is built without the use of any resistors. Furthermore, a second-order low-pass filter based on this CNIC is also analysed. It shows a bandwidth of 50 MHz at 320 µW power consumption and 2 V supply voltage when realized in a 0.35 µm CMOS process.

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Authors and Affiliations

W. Jendernalik
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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

Tadeusz Kaczorek
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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

Necessary and sufficient conditions for the reachability and observability of the positive electrical circuits composed of resistors, coils, condensators and voltage sources are established. Definitions of the input-decoupling zeros, output-decoupling zeros and input-output decoupling zeros of the positive electrical circuits are proposed. Some properties of the decoupling zeros of positive electrical circuits are discussed.

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Authors and Affiliations

Tadeusz Kaczorek
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Abstract

The positivity of descriptor continuous-time and discrete-time linear systems with regular pencils are addressed. Such systems can be reduced to standard linear systems and can be decomposed into dynamical and static parts. Two definitions of the positive systems are proposed. It is shown that the definitions are not equivalent. Conditions for the positivity of the systems and the relationship between two classes of positive systems are established. The considerations are illustrated by examples of electrical circuits and numerical examples.

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Authors and Affiliations

Tadeusz Kaczorek
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Abstract

The minimum energy control problem for the positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.

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Authors and Affiliations

Tadeusz Kaczorek
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Abstract

New frequency domain methods for stability analysis of linear continuous-time fractional order systems with delays of the retarded type are given. The methods are obtained by generalisation to the class of fractional order systems with delays of the Mikhailov stability criterion and the modified Mikhailov stability criterion known from the theory of natural order systems without and with delays. The study is illustrated by numerical examples of time-delay systems of commensurate and non-commensurate fractional orders.

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Authors and Affiliations

M. Busłowicz
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Abstract

The positivity of fractional descriptor linear continuous-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear continuous-time systems are established. The considerations are illustrated by numerical examples.

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Authors and Affiliations

T. Kaczorek
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Abstract

This paper is devoted to some problems that appear in derivations of the discrete time Fourier transform from a formula for its continuous time counterpart for transformation from the time into the frequency domain as well as to those regarding transformation in the inverse direction. In particular, the latter ones remained so far an unresolved problem. It is solved for the first time here. Many detailed explanations accompanying the solution found are presented. Finally, it is also worth noting that our derivations do not exploit any of such sophisticated mathematical tools as the so-called Dirac delta and Dirac comb.

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Authors and Affiliations

Andrzej Borys
ORCID: ORCID
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Abstract

The asymptotic stability of positive descriptor continuous-time and discrete-time linear systems is considered. New sufficient conditions for stability of positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of continuous-time and discrete-time linear systems.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID

  1. Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok, Poland
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Abstract

The concepts of full-order and reduced-order observers are extended to the fractional linear continuous-time systems. Necessary and sufficient conditions for the existence of the observers for fractional linear systems are established. Procedures for designing of the observers are given and illustrated by examples.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID

  1. Białystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
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Abstract

The positivity and absolute stability of a class of nonlinear continuous-time and discretetime systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of nonlinear systems are also given.

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Authors and Affiliations

Tadeusz Kaczorek
ORCID: ORCID
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Abstract

The asymptotic stability of fractional positive descriptor continuous-time and discretetime linear systems is considered. New sufficient conditions for stability of fractional positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of fractional continuous-time and discrete-time linear systems.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID
Andrzej Ruszewski
1
ORCID: ORCID

  1. Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
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Abstract

The asymptotic stability of the convex linear combination of continuous-time and discretetime linear systems is considered. Using the Gershgorin theorem it is shown that the convex linear combination of the linear asymptotically stable continuous-time and discretetime linear systems is also asymptotically stable. It is shown that the above thesis is also valid (even simpler) for positive linear systems.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID

  1. Bialystok University of Technology, Faculty ofElectrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
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Abstract

In the paper, a general topology of continuous-time Active-RC filter is presented. The model includes all possible Active-RC filter

structures as particular cases and allows us to analyze them using a unified algebraic formalism. This makes it suitable for use in computeraided analysis and design of Active-RC filters. By its construction, the model takes into account the finite DC gain and the finite bandwidth as well as non-zero output resistance of operational amplifiers. Filters with ideal OPAMPs can be treated as particular cases. Sensitivity and noise analysis of Active-RC filters is also performed in the proposed general setting. The correctness of the model is verified by comparison with SPICE simulation.

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Authors and Affiliations

S. Kozieł
S. Szczepański
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Abstract

The paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned ‘integrating filters’ of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization and can be identified, for example, by the classical least squares procedure. Since in the presence of correlated noise, the estimated parameter values are burdened with an unavoidable systematic error (manifested by asymptotic bias of the estimates), in order to significantly improve the identification consistency, the method of instrumental variables is used here. In our research we use an estimation algorithm based on the least absolute values (LA) criterion of the least sum of absolute values, which is optimal in identifying linear and non-linear systems in the case of sporadic measurement errors. In the paper, we propose a procedure for determining the instrumental variable for a continuous model with non-linearity (related to the Wienerian system) in order to remove the evaluation bias, and a recursive sub-optimal version of the LA estmator. This algorithm is given in a simple (LA) version and in an instrumental variable version (IV-LA), which is robust to outliers, removes evaluation bias, and is suited to the task of identifying processes with non-linear dynamics (semi-Wienerian/NLID). In conclusion, the effectiveness of the proposed algorithmic solutions has been demonstrated by numerical simulations of the mechanical system, which is an essential part of the suspension system of a wheeled vehicle.
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Authors and Affiliations

Janusz Kozłowski
1
ORCID: ORCID
Zdzisław Kowalczuk
1
ORCID: ORCID

  1. Gdansk University of Technology, WETI, Narutowicza 11/12, 80-952 Gdańsk
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Abstract

Glass production has a great industrial importance and is associated with many technological challenges. Control related problems concern especially the last part of the process, so called glass conditioning. Molten glass is gradually cooled down in a long ceramic channels called forehearths during glass conditioning. The glass temperature in each zone of the forehearth should be precisely adjusted according to the assumed profile. Due to cross-couplings and unmeasured disturbances, traditional control systems based on PID controllers, often do not ensure sufficient control quality. This problem is the main motivation for the research presented in the paper. A Model Predictive Control algorithm is proposed for the analysed process. It is assumed the dynamic model for each zone of the forehearth is identified on-line with the Modulating Functions Method. These continuous-time linear models are subsequently used for two purposes: for the predictive controller tuning, measurable disturbances compensation and for a static set point optimisation. Proposed approach was tested using Partial Differential Equation model to simulate two adjacent zones of the forehearth. The experimental results proved that it can be successfully applied for the aforementioned model.
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Authors and Affiliations

Michał Drapała
1
Witold Byrski
1

  1. Department of Automatic Control and Robotics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
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Abstract

Software vulnerability life cycles illustrate changes in detection processes of software vulnerabilities during using computer systems. Unfortunately, the detection can be made by cyber-adversaries and a discovered software vulnerability may be consequently exploited for their own purpose. The vulnerability may be exploited by cyber-criminals at any time while it is not patched. Cyber-attacks on organizations by exploring vulnerabilities are usually conducted through the processes divided into many stages. These cyber-attack processes in literature are called cyber-attack live cycles or cyber kill chains. The both type of cycles have their research reflection in literature but so far, they have been separately considered and modeled. This work addresses this deficiency by proposing a Markov model which combine a cyber-attack life cycle with an idea of software vulnerability life cycles. For modeling is applied homogeneous continuous time Markov chain theory.
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Authors and Affiliations

Romuald Hoffmann
1

  1. Institute of Computer and Information Systems, Faculty of Cybernetics, Military University of Technology, Warsaw, Poland
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Abstract

The Lagrange-Sylvester formula is applied to the computation of the solutions of state equations of fractional continuous-time and discrete-time linear systems. The solutions are given as finite sums with their numbers of components equal to the degrees of the minimal characteristics polynomials of state matrices of the systems. Procedures for computations of the solutions are given and illustrated by numerical examples of continuous-time and discrete-time fractional linear systems.
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Bibliography

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  4.  T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin, 2011.
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  8.  T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. Circuits Syst. 58(7), 1203‒1210 (2011).
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  10.  T. Kaczorek, “Stability of fractional positive nonlinear systems”, Arch. Control Sci. 25(4), 491‒496 (2015).
  11.  A. Ruszewski, “Stability of discrete-time fractional linear systems with delays”, Arch. Control Sci. 29(3), 549‒567 (2019).
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  13.  Ł. Sajewski, “Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller”, Bull. Pol. Acad. Sci. Tech. Sci. 65(5), 709‒714 (2017).
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID

  1. Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D, 15-351 Białystok, Poland

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