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1

Zeroing the transfer matrix of the Roesser model of 2-D linear systems

Kaczorek Tadeusz

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 4

513--519

EN

Controllability, observability and the transfer matrix of the discrete 2-D Roesser model are analyzed. It is shown that the controllability of the Roesser model is invariant under state feedbacks and the observability under output feedbacks. Sufficient conditions are established for the zeroing of the transfer matrix of the Roesser model.

2

Standard and fractional discrete-time linear systems with zero transfer matrices

Kaczorek Tadeusz, Ruszewski Andrzej

Acta Mechanica et Automatica

|

2023

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Vol. 17, no. 2

188--191

EN

The transfer matrix of the standard and fractional linear discrete-time linear systems is investigated. Necessary and sufficient conditions for zeroing of the transfer matrix of the linear discrete-time systems are established. The considerations are illustrated by examples of the standard and fractional linear discrete-time systems.

3

Some analysis problems of the linear systems

Kaczorek Tadeusz

Journal of Automation, Electronics and Electrical Engineering

|

2022

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Vol. 4, No. 2

7--12

EN

New approaches to the transformations of the uncontrollable and unobservable matrices of linear systems to their canonical forms are proposed. It is shown that the uncontrollable pair (A,B) and unobservable pair (A,C) of linear systems can be transform to their controllable (𝐴̅ , 𝐵̅ ) and observable (𝐴̅ , 𝐶̅ ) canonical forms by suitable choice of nonsingular matrix M satisfying the condition 𝑀[𝐴 𝐵] = [𝐴̅ 𝐵̅ ] and [𝐴 𝐵]𝑀 = [𝐴̂ 𝐵̂ ], respectively. It is also shown that by suitable choice of the gain matrix K of the feedbacks of the derivative of the state vector it is possible to reduce the descriptor system to the standard one.

PL

Zaproponowano nowe podejścia do transformacji niesterowalnych i nieobserwowalnych macierzy układów liniowych do ich postaci kanonicznych. Wykazano, że niesterowalna para (A,B) i nieobserwowalna para (A,C) układów liniowych może być przekształcona do ich postaci kanonicznych sterowalnych i obserwowalnych prze odpowiedni dobór nieosobliwej macierzy M spełniającej warunki 𝑀[𝐴 𝐵] = [𝐴̅ 𝐵̅ ] i [𝐴 𝐵]𝑀 = [𝐴̂ 𝐵̂ ]. Pokazano,żeprzezodpowiednidobórmacierzyKsprzężeniazwrotnego od pochodnej wektora stanu jest możliwa redukcja układu deskryptorowegodoukładustandardowego.

4

Invariance of reachability and observability for fractional positive linear electrical circuit with delays

Yuan Tong, Yang Hongli

Archives of Electrical Engineering

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2021

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Vol. 70, nr 3

513--530

EN

This paper focuses on the invariance of the reachability and observability for fractional order positive linear electrical circuits with delays and their checking methods. By derivation and comparison, it shows that conditions and checking methods of reachability and observability for integer and fractional order positive linear electrical circuits with delays are invariant. An illustrative example is presented at the end of the paper.

5

An output sensitivity problem for a class of linear distributed systems with uncertain initial state

Larrache Abdelilah, Lhous Mustapha, Rhila Soukina Ben, Rachik Mostafa, Tridane Abdessamad

Archives of Control Sciences

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2020

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Vol. 30, No. 1

139--155

EN

In this paper,we consider an infinite dimensional linear systems. It is assumed that the initial state of system is not known throughout all the domain Ω C Rn, the initial state x0 ϵ L2(Ω) is supposed known on one part of the domain Ω and uncertain on the rest. That means Ω = ω1 U ω2 U... U ωt with ωi ∩ ωj = ∅, ∀i ≠ j ϵ {1,...,t}, i ≠ j where ωi ≠ ∅ and x0(θ) = αi for θ ϵ ωi, ∀i, i.e., x0(θ) = [wzór] (θ) where the values α1,...,αr are supposed known and αr+1,...,αt unknown and 1ωi is the indicator function. The uncertain part (α1,...,(α)rof the initial state x0 is said to be (ɛ1,...,ɛr )-admissible if the sensitivity of corresponding output signal (yi)i≥0 relatively to uncertainties (αk)1≤k≤r is less to the treshold ɛk, i.e., ∥∂yi)/(∂αk∥ ≤ ɛk, ∀i≥ 0, ∀k ϵ {1,...,r]. The main goal of this paper is to determine the set of all possible gain operators that makes the system insensitive to all uncertainties. The characterization of this set is investigated and an algorithmic determination of each gain operators is presented. Some examples are given.

6

Independence of the controllability and observability of resistances in linear electrical circuits

Kaczorek Tadeusz

Journal of Automation, Electronics and Electrical Engineering

|

2019

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Vol. 1, No. 1

9--15

EN

Sufficient conditions are given under which the controllability and observability of linear electrical circuits is independent of their resistances. In some particular cases the observability depends only on the capacitances or inductances of the electrical circuits.

7

State estimation of networked control systems over limited capacity and dropout channels

Liu Qingquan, Ding Rui, Chen Chunqiang

Archives of Control Sciences

|

2019

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Vol. 29, No. 4

687--697

EN

This paper investigates state estimation of linear time-invariant systems where the sensors and controllers are geographically separated and connected over limited capacity, additive white Gaussian noise (AWGN) communication channels. Such channels are viewed as dropout (erasure) channels. In particular, we consider the case with limited data rates, present a necessary and sufficient condition on the data rate for mean square observability over an AWGN channel. The system is mean square observable if the data rate of the channel is larger than the lower bound given. It is shown in our results that there exist the inherent tradeoffs among the limited data rate, dropout probability, and observability. An illustrative example is given to demonstrate the effectiveness of the proposed scheme.

8

Compliance in Business Processes with Incomplete Information and Time Constraints : a General Framework based on Abductive Reasoning

Chesani F., Mello P., Montali M., Tessaris S., De Masellis R., Di Francescomarino C., Ghidini C.

Fundamenta Informaticae

|

2018

|

Vol. 161, nr 1/2

75--111

EN

The capability to store data about Business Process (BP) executions in so-called Event Logs has brought to the identification of a range of key reasoning services (consistency, compliance, runtime monitoring, prediction) for the analysis of process executions and process models. Tools for the provision of these services typically focus on one form of reasoning alone. Moreover, they are often very rigid in dealing with forms of incomplete information about the process execution. While this enables the development of ad hoc solutions, it also poses an obstacle for the adoption of reasoning-based solutions in the BP community. In this paper, we introduce the notion of Structured Processes with Observability and Time (SPOT models), able to support incompleteness (of traces and logs), and temporal constraints on the activity duration and between activities. Then, we exploit the power of abduction to provide a flexible, yet computationally effective framework able to reinterpret key reasoning services in terms of incompleteness and observability in a uniform way.

9

Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices

Kaczorek T.

Archives of Control Sciences

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2018

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Vol. 28, No. 1

119--133

EN

The notions of monomial generalized Frobenius matrices is proposed and the reachability and observability of positive discrete-time linear systems with positive and negative integer powers of the state matrices is addressed. Necessary and sufficient conditions for the reachability of the positive systems are established.

10

Problems of designing state feedback controllers for objects with transfer function zeros

Drozdov V., Abdullin A., Mamatov A.

Power Electronics and Drives

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2017

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Vol. 2 (37), No. 2

77--92

EN

The analysis of the influence of transfer function zeros on the parameters of state feedback controllers has been conducted. If a transfer function of a control object has zeros which are located closely to poles, the control object tends to singularity, and the influence of the input control signal to the states of the control object becomes weaker. The problem of the state feedback controller synthesis becomes ill-conditioned, which leads to the appearance of extremely large state feedback coefficients. In this case, the state feedback coefficients are sensitive to the parameters of the control object. As a result, the parametric robustness of the control system is reduced. Known methods of structural analysis of control object models are included amongst different methods of the numerical evaluation of the controllability and the observability, as well as methods of the model order reduction. These methods have some disadvantages, such as dependence on the state space representation form of the control object, ignoring a part of the control object model. In this paper, some ways of the preliminary structural analysis of the state space models of control objects have been proposed. The singular (Hankel) matrix is proposed for analyzing the properties of control object models. The singular matrix is the invariant characteristic of the control object in various state space forms and it characterizes the property of the control object completeness. As a result of the research, it was found that the coefficients of the state feedback controller are inversely proportional to the determinant of the singular matrix, and the determinant of the singular matrix is equal to the resultant of the transfer function polynomials. Thus the value of the determinant of the singular matrix depends on the location of the zeros of the transfer function. The method of the structural transformation (decomposition) of the control object for the defining the need of the reducing the order of the control object model is proposed.

11

A remark on observability of the wave equation with moving boundary

Ammari K., Bchatnia A., El Mufti K.

Journal of Applied Analysis

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2017

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Vol. 23, nr 1

43--51

EN

We deal with thewave equation with assigned moving boundary (0 < x < a(t)) uponwhich Dirichlet or mixed boundary conditions are specified. Here a(t) is assumed to move slower than light and periodically. Moreover, a is continuous, piecewise linear with two independent parameters. Our major concern will be an observation problem which is based measuring, at each t > 0, of the transverse velocity at a(t). The key to the results is the use of a reduction theorem by Yoccoz [14].

12

On controllability and observability of fractional continuous-time linear systems with regular pencils

Younus A., Javaid I., Zehra A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2017

|

Vol. 65, nr 3

297--304

EN

In this paper necessary and sufficient conditions of controllability and observability for solutions of the state equations of fractional continuous time linear systems with regular pencils are proposed. The derivations of the conditions are based on the construction of Gramian matrices.

13

Relationship between the observability of standard and fractional linear systems

Kaczorek T.

Archives of Control Sciences

|

2017

|

Vol. 27, no. 3

441--451

EN

The relationship between the observability of standard and fractional discrete-time and continuous-time linear systems are addressed. It is shown that the fractional discrete-time and continuous-time linear systems are observable if and only if the standard discrete-time and continuous-time linear systems are observable.

14

Solving the problem of distribution network observability with smart meters

Golub I. I., Kuzkina Y. I.

Acta Energetica

|

2017

|

nr 4

4--9

EN

The paper is concerned with the problem of choice of the minimum number of smart meters to ensure either the observability of all state variables in distribution network or the observability of voltage magnitudes whose control is particularly important in the low voltage distribution networks with distributed generation. Currently only voltage magnitudes, active and reactive currents can be synchronized. It is shown that replacement of voltage phasor measurements with the measurements of voltage magnitudes alone makes it possible to provide observability of voltage magnitudes at all feeder nodes with the number of smart meters lower than the number of load nodes.

PL

Artykuł dotyczy problemu wyboru minimalnej liczby liczników inteligentnych, wystarczającej do zapewnienia obserwowalności wszystkich zmiennych stanu sieci rozdzielczej lub wartości napięcia, którego regulacja jest szczególnie ważna w sieciach rozdzielczych niskiego napięcia z generacją rozproszoną. Pokazano, że samo zastąpienie pomiarów fazorów napięcia pomiarami wartości amplitudy napięcia umożliwia zapewnienie obserwowalności wartości amplitudy napięcia we wszystkich węzłach zasilających przy liczbie liczników inteligentnych mniejszej niż liczba węzłów odbiorczych.

15

Standard and positive electrical circuits with zero transfer matrices

Kaczorek T.

Poznan University of Technology Academic Journals. Electrical Engineering

|

2016

|

No. 85

11--28

EN

Standard and positive electrical circuits with zero transfer matrices are addressed. It is shown that there exists a large class of electrical circuits composed of resistances, inductances, capacitances and voltage (current) sources with zero transfer matrices. The electrical circuits are unreachable, unobservable and unstable for all values of the resistances, inductances and capacitances. An extension of these considerations to fractional electrical circuits is given.

16

Positive electrical circuits with zero transfer matrices and their discretization

Kaczorek T.

Computer Applications in Electrical Engineering

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2016

|

Vol. 14

1--13

EN

Positive continuous–time and discrete–time linear electrical circuits with zero transfer matrices are addressed. It is shown that there exists a large class of positive electrical circuits with zero transfer matrices. The electrical circuits are unreachable, unobservable and unstable for all values of the resistances, inductances and capacitances. The discrete–time linear positive electrical circuits are introduced. It is shown that: 1) the discrete–time electrical circuit is asymptotically stable for all values of the discretization step if and only if the corresponding continuous–time electrical circuit is asymptotically stable; 2) the discretization of the continuous–time electrical circuit does not change their reachability, observability and transfer matrices.

17

Observability and controllability analysis for sandwich systems with backlash

Luo N., Tan Y., Dong R.

International Journal of Applied Mathematics and Computer Science

|

2015

|

Vol. 25, no. 4

803--814

EN

In this paper, an approach to analyze the observability and controllability of sandwich systems with backlash is proposed. In this method, a non-smooth state-space function is used to describe the sandwich systems with backlash which are also non-smooth non-linear systems. Then, a linearization method based on non-smooth optimization is proposed to derive a linearized state-space function to approximate the non-smooth sandwich systems within a bounded region around the equilibrium point that we are interested in. Afterwards, both observability and controllability matrices are constructed and the methods to analyze the observability as well as controllability of sandwich system with backlash are derived. Finally, numerical examples are presented to validate the proposed method.

18

q-nonuniform difference linear control systems

Bangerezako G

Journal of Applied Analysis

|

2014

|

Vol. 20, nr 2

133--143

EN

We introduce q-nonuniform difference systems and propose q-nonuniform versions of some basic results of complete controllability and observability of linear systems such as criterions of controllability and observability, the q-duality theorem. An optimality necessary condition is also given for the case of the Ramsey model of economic growth.

19

Monitoring Changes in Dynamic Multiset Systems

Ciobanu G., Sburlan D.

Fundamenta Informaticae

|

2014

|

Vol. 134, nr 1/2

67--82

EN

Models of biological systems expressed as multiset rewriting systems can be very complex, impeding the analysis of their behaviour. In this paper we propose a practical solution to this problem, in the form of change monitors, i.e. computational instruments which synchronise with the model and record its behaviour. Change monitors play the role of passive observers. Since change monitors can automatically identify specific behaviours generated by the model under investigation, it is sufficient to focus only on the output produced by the monitors (instead of examining the dynamics of the initial model).

20

Remarks on the Stabilization Problem for Linear Finite-Dimensional Systems

Nambu T.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2014

|

Vol. 62, no 1

87--99

EN

The celebrated 1967 pole assignment theory of W. M. Wonham for linear finite-dimensional control systems has been applied to various stabilization problems both of finite and infinite dimension. Besides existing approaches developed so far, we propose a new approach to feedback stabilization of linear systems, which leads to a clearer and more explicit construction of a feedback scheme.