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1
Content available remote Positivity and stabilization of fractional 2D linear systems described by the Roesser model
Kaczorek T., Rogowski K.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 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.
2
Content available remote Independence of asymptotic stability of positive 2D linear systems with delays of their delays
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
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Vol. 19, no 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.
3
Content available remote Positive realization for 2D systems with delays
Kaczorek T.
Pomiary Automatyka Robotyka
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2007
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R. 11, nr 2
EN
Realization problem for positive single-input single-output systems with delays in state vector and inputs described by the 2D models is addressed. Sufficient condition for the existence of a positive realization are established and a procedure for finding a positive realization for a given proper transfer function is proposed. The procedure is illustrated by a numerical example.
PL
W pracy podano metodę wyznaczania dodatniej realizacji układów dwuwymiarowych (2D) o jednym wejściu i jednym wyjściu z opóźnieniami w wektorze stanu i wymuszeniu. Podano warunki wystarczające na istnienie realizacji dodatnich oraz procedurę wyznaczania realizacji dodatnich dla danej właściwej transmitancji operatorowej. Procedurę zilustrowano przykładem numerycznym.
4
Content available remote Robust stabilization of discrete linear repetitive processes with switched dynamics
Bochniak J., Gałkowski K., Rogers E., Kummert A.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 4
441-462
EN
Repetitive processes constitute a distinct class of 2D systems, i.e., systems characterized by information propagation in two independent directions, which are interesting in both theory and applications. They cannot be controlled by a direct extension of the existing techniques from either standard (termed 1D here) or 2D systems theories. Here we give new results on the design of physically based control laws. These results are for a sub-class of discrete linear repetitive processes with switched dynamics in both independent directions of information propagation.
5
Content available remote Determination of reachability subspace of two-dimensional positive linear systems described by Roesser model
Markowski K.A.
Przegląd Elektrotechniczny
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2005
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R. 81, nr 3
89-92
EN
A method of determinination reachability subspace of the positive two dimension systems described by Roesser model using digraph theory is proposed. A procedure for computation of the reachability subspace is also proposed. The procedure illustrated by a numerical example.
PL
Przedstawiono metodę wyznaczania obszaru osiągalności dodatnich układów dwuwymiarowych opisanych za pomocą modelu Roessera. Zaproponowaną procedurę zilustrowano prostym przykładem numerycznym.
6
Content available remote On the Interaction Between Theory, Experiments, and Simulation in Developing Practical Learning Control Algorithms
Longman R. W.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 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.
7
Content available remote An Application of the Fourier Transform to Optimization of Continuous 2-D Systems
Dymkou V., Dymkov M.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 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.
8
Content available Minimal order deadbeat functional observers for singular 2D linear systems
Kaczorek T.
Control and Cybernetics
|
2003
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Vol. 32, no 2
301-311
EN
Sufficient conditions for the existence of minimal order deadbeat functional observers for singular 2D linear systems described by the general singular 2D model are established. A procedure for computing matrices of the functional observers is given and illustrated by numerical example.
9
Content available remote Controllability of Nonlinear Discrete Systems
Klamka J.
International Journal of Applied Mathematics and Computer Science
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2002
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Vol. 12, no 2
173-180
EN
Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear discrete systems with constrained controls.
10
Content available An algebraic analysis approach to 2-D discrete problems
Przeworska-Rolewicz D., Wysocki H.
Control and Cybernetics
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2001
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Vol. 30, no 2
149-158
EN
A model of algebraic analysis for the 2-index sequences (of the type 2-D) is considered. For difference operators of the form D{x_m,n}:= {x_m+1,n+1 - A_m,nX_m,n} the right inverses and the corresponding initial operators are constructed. Having already known the initial operators, one can determine solutions of the corresponding initial value problems.
11
Content available remote Linear 2-D Systems of the Siepiński Gasket Type
Trzaska Z.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2000
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Vol. 48, nr 1
29-39
EN
The paper is aimed on 2-D models for fractal linear structures composed of identical passive elements and connected into the Sierpiński triangle. A new approach for evaluation of the distribution of appropriate signals within the whole structure is established. The efficiency of the method is demonstrated and well proved. Distinguished properties of the established distribution are demonstrated. Illustrative example is also presented.
12
Content available remote Non-standard State-space Models for 2D Systems
Gałkowski K., Theodorou N., Tzafestas S.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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1999
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Vol. 47, nr 1
91-101
EN
In this paper, non-standard 2D state space models of the Roesser type and their equivalence under similarity and elementary operations are discussed. Non-standard models cover a wider repertory of systems than traditional ones of both theoretical and practical importance.
13
Content available remote Local Controllability of 2D Nonlinear Systems
Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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1999
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Vol. 47, nr 2
153-162
EN
In the present paper local constrained controllability problems for nonlinear discrete 2D system with constant coefficients and constrained controls are formulated and discussed. Using some mapping theorems taken from functional analysis and linear approximation methods sufficient conditions for constrained controllability are derived and proved. The present paper extends in some previous results given in the literature to cover controllability problem for the nonlinear discrete 2D systems with constant coefficients and constrained controls.
14
Content available remote Controllability of 2D continuous-discrete systems with delays in control
Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
1998
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Vol. 46, nr 3
363-373
EN
Recently, a new class of linear continuous-discrete 2D dynamical systems i.e., dynamical systems described by the indexed set of linear ordinary differential equations with appropriate initial and boundary conditions has been introduced. However, it should be mentioned that only a few papers deal with the 2D continuous-discrete linear dynamical systems with delays. In linear 2D continuous-discrete dynamical systems one independent variable is continuous and the second one is discrete. Such continuous-discrete models appear, for example, in the iterative learning control systems. Another example of such systems are the repetitive processes. In the present paper linear 2D continuous-discrete systems with multiple constant delays in the control and constant coefficients are considered. The general response formula for such 2D systems is derived. Fundamental definition of relative controllability in a given fixed rectangle is presented. Using some theorems taken from the theory of linear dynamical systems with delays in the state variable necessary and sufficient pure algebraic rank condition for relative controllability is formulated and proved. Moreover, remarks and comments on controllability of 2D linear continuous-discrete dynamical systems are given.
15
Content available remote Constrained controllability of positive 2D systems
Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
1998
|
Vol. 46, nr 1
95-104
EN
In this paper we examine the issue of controllability for positive linear 2D systems. We look at the connections between reachability, reach ability from zero boundary conditions, and the rank criterion for controllability for systems in which both the state and controls are constrained by practical considerations to lie in a positive orthant. While these concepts are equivalent for unconstrained systems, there are significant changes in the positive case. We analyse these differences and show how they affect control strategy. Example, which illustrates theoretical results is also given.
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