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1
Content available On Derivation of Discrete Time Fourier Transform from Its Continuous Counterpart
Borys Andrzej
International Journal of Electronics and Telecommunications
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2020
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Vol. 66, No. 2
355-360
EN
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.
2
Content available State estimation for miso non-linear systems in controller canonical form
Schwaller B., Ensminger D., Dresp-Langley B., Ragot J.
International Journal of Applied Mathematics and Computer Science
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2016
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Vol. 26, no. 3
569--583
EN
We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.
3
Content available Fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative
Kaczorek T., Borawski K.
International Journal of Applied Mathematics and Computer Science
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2016
|
Vol. 26, no. 3
533--541
EN
The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
4
Content available State estimation for a class of nonlinear systems
Schwaller B., Ensminger D., Dresp-Langley B., Ragot J.
International Journal of Applied Mathematics and Computer Science
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2013
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Vol. 23, no. 2
383--394
EN
We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of non-linearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin’s damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example.
5
Content available Minimum energy control of positive continuous-time linear systems with bounded inputs
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2013
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Vol. 23, no. 4
725--730
EN
The minimum energy control problem for positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
6
Content available Asynchronous distributed state estimation for continuous-time stochastic processes
Kowalczuk Z., Domżalski M.
International Journal of Applied Mathematics and Computer Science
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2013
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Vol. 23, no. 2
327--339
EN
The problem of state estimation of a continuous-time stochastic process using an Asynchronous Distributed multi-sensor Estimation (ADE) system is considered. The state of a process of interest is estimated by a group of local estimators constituting the proposed ADE system. Each estimator is based, e.g., on a Kalman filter and performs single sensor filtration and fusion of its local results with the results from other/remote processors to compute possibly the best state estimates. In performing data fusion, however, two important issues need to be addressed namely, the problem of asynchronism of local processors and the issue of unknown correlation between asynchronous data in local processors. Both the problems, along with their solutions, are investigated in this paper. Possible applications and effectiveness of the proposed ADE approach are illustrated by simulated experiments, including a non-complete connection graph of such a distributed estimation system.
7
Content available A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2012
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Vol. 22, no. 4
897-905
EN
A new modified state variable diagram method is proposed for determination of positive realizations of linear continuous-time systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.
8
Content available Modelling CTMC with a standard programming language and using conventions from computer networking
Rataj A., Nowak M., Pecka P.
Theoretical and Applied Informatics
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2011
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Vol. 23, No. 3-4
229-243
EN
Continuous time Markov chains (CTMC) are one of the formalisms for building models. This paper discusses expressing these models in a standard programming language – Java. Using such a language as a model description allows for a partially common implementation of the production software and of the description of the model, for a greater flexibility in comparison to model-checker specific languages that often do not employ features of an object-oriented programming. Using Java also makes the parsing of models relatively fast, using optimised Java runtime environment. Our approach aims at using typical mechanisms of the Java language when implementing the model, and at the same time, following closely the concepts from computer networking and from formalisms based on it, like the queueing systems. These assumption result in techniques like plain object fields constituting the state vector, or negotiation between nodes to decide if an event happens.
PL
Łańcuchy Markowa czasu rzeczywistego są jednym z formalizmów używanych do budowy modeli. Artykuł ten omawia wyrażanie takich modeli w standardowym języku programowania - Javie. Użycie takiego języka umożliwia częściowo wspólną implementację oprogramowania użytkowego i opisu modelu, większą elastyczność w porównaniu do często nie używających obiektowych konwencji programistycznych języków stosowanych przez oprogramowanie weryfikujące, oraz szybką budowę modelu z użyciem zoptymalizowanego środowiska czasu wykonania Javy. Nasze podejście miało na celu wykorzystanie typowych mechanizmów języka Java przy opisie modelu i jednoczesnie trzymanie się konwencji z dziedziny sieci komputerowych i pokrewnych formalizmóm typu systemy kolejkowe. Dlatego używamy technik takich jak zastosowanie pól obiektów jako elementów wektora stanu czy negocjacja pomiędzy węzłami, czy dane zdarzenie ma mieć miejsce.
9
Content available remote On the alternative stability criteria for positive systems
Twardy M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2007
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Vol. 55, nr 4
379-383
EN
The paper discusses the stability problem for continuous time and discrete time positive systems. An alternative formulation of stability criteria for positive systems has been proposed. The results are based on a theorem of alternatives for linear matrix inequality (LMI) feasibility problem, which is a particular case of the duality theory for semidefinite programming problems.
10
Content available remote Extension of The Cayley-Hamilton Theorem to Continuous-time Linear Systems With Delays
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2005
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Vol. 15, no 2
231-234
EN
The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices $A_0, A_1, dots, A_h in R^{n times n}$ of the system with $h$ delays $dot xleft(t right) = A_0 xleft(t right) + sum_{i = 1}^h {A_i xleft( {t - hi} right) + Buleft( t right)}$ satisfy $nh + 1$ algebraic matrix equations with coefficients of the characteristic polynomial $pleft( {s,w}right) = det left[ {I_n s - A_0 - A_1 w - cdots - A_h w^h }right]$, $w = e^{- hs}$.
11
Content available remote Identification of Low-Order Continuous-Time Models Via Discrete-Time Trends of Measurements
Janiszowski K. B.
International Journal of Applied Mathematics and Computer Science
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1999
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Vol. 9, no 4
839-853
EN
The paper deals with the problem of continuous-time (CT) identification of parameters in transfer functions for low-order linear systems, based on recorded discrete-time (DT) data. Algorithms for direct estimation of CT parameters are developed from rules for transformation of a CT transferfunction controlled via a zero-order sampling-and-hold unit into a DT representation.Two schemes are derived and tested: the first is based on the Goodwin transformation and the other is derived from the modified Tustin transformation. Both the approaches result in relations which can be used for direct estimationof CT parameters in a model of the investigated system. The numerical schemes contain some expressions that are reminiscent of DT differences and consequently they may magnify disturbances. Therefore the results of extensively testing both the schemes including different types of disturbances, measurement noise, slow varying drifts, measurement resolution errors together with changes in the sampling time are presented. A model of a pneumatic servomechanism system was used as a test plant.
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