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Independence of asymptotic stability of positive 2D linear systems with delays of their delays

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 2
255-261
EN
It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.
2
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On the interaction between theory experiments and simulation in developing practical learning control algorithms

100%
Longman R. W.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 1
101-111
EN
Iterative learning control (ILC) develops controllers that iteratively adjust the command to a feedback control system in order to converge to zero tracking error following a specific desired trajectory. Unlike optimal control and other control methods, the iterations are made using the real world in place of a computer model. If desired, the learning process can be conducted both in the time domain during each iteration and in repetitions, making ILC a 2D system. Because ILC iterates with the real world, and aims for zero error, the field pushes the limits of theory, modeling, and simulation, to predict the behavior when applied in the real world. It is the thesis of this paper that in order to make significant progress in this field it is essential that the research effort employ a coordinated simultaneous synergistic effort involving theory, experiments, and serious simulations. Otherwise, one very easily expends effort on something that seems fundamental from the theoretical perspective, but in fact has very little relevance to the performance in real world applications.
3
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An application of the Fourier transform to optimization of continuous 2-D systems

88%
Dymkou V., Dymkov M.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 1
45-54
EN
This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.
4
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Positivity and stabilization of fractional 2D linear systems described by the Roesser model

88%
Kaczorek T., Rogowski K.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 1
85-92
EN
A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.
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