PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 8

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  discrete time system
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Discrete-time output observers for boundary control systems
Emirsajłow Zbigniew
International Journal of Applied Mathematics and Computer Science
|
2021
|
Vol. 31, no. 4
613--626
EN
The paper studies the output observer design problem for a linear infinite-dimensional control plant modelled as an abstract boundary input/output control system. It is known that such models lead to an equivalent state space description with unbounded control (input) and observation (output) operators. For this class of infinite-dimensional systems we use the Cayley transform to approximate the sophisticated infinite-dimensional continuous-time model by a discrete-time infinite-dimensional one with all involved operators bounded. This significantly simplifies mathematical aspects of the observer design procedure. As is well known, the essential feature of the Cayley transform is that it preserves various system theoretic properties of the control system model, which may be useful in analysis. As an illustration, we consider an example of designing an output observer for the one-dimensional heat equation with measured controls (inputs) in the Neumann boundary conditions, measured outputs in the Dirichlet boundary conditions and an unmeasured output at a fixed point within the domain. Numerical simulations of this example show that the interpolated continuous-time signal, obtained from the discrete-time observer, can be successfully used for tracking the continuous-time plant output.
2
Content available Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
Grzymkowski Łukasz, Trofimowicz Damian, Stefański Tomasz P.
International Journal of Applied Mathematics and Computer Science
|
2020
|
Vol. 30, no. 4
649--658
EN
In this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained theoretical results lead to a numerical test for stability evaluation of interconnected FO systems. It is based on modern root-finding techniques on the complex plane employing triangulation of the unit circle and Cauchy’s argument principle. The developed numerical test is simple, intuitive and can be applied to a variety of systems. Furthermore, because it evaluates the function related to the characteristic equation on the complex plane, it does not require computation of state-matrix eigenvalues. The obtained numerical results confirm the efficiency of the developed test for the stability analysis of interconnected discrete-time FO LTI state-space systems.
3
Content available Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication
Djennoune Said, Bettayeb Maamar, Al-Saggaf Ubaid Muhsen
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 1
179--194
EN
This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.
4
Content available Positivity of fractional descriptor linear discrete-time systems
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 2
305--310
EN
The positivity of fractional descriptor linear discrete-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 discrete-time systems are established. The discussion is illustrated with numerical examples.
5
Content available Parameter identification and estimation for stage-structured population models
Coll Carmen, Sánchez Elena
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 2
327--336
EN
A stage-structured population model with unknown parameters is considered. Our purpose is to study the identifiability of the model and to develop a parameter estimation procedure. First, we analyze whether the parameter vector can or cannot uniquely be determined with the knowledge of the input-output behavior of the model. Second, we analyze how the information in the experimental data is translated into the parameters of the model. Furthermore, we propose a process to improve the recursive values of the parameters when successive observation data are considered. The structure of the state matrix leads to an analysis of the inverse of a sum of rank-one matrices.
6
Content available A reference trajectory based discrete time sliding mode control strategy
Bartoszewicz Andrzej, Adamiak Katarzyna
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 3
517--525
EN
This study presents a new, reference trajectory based sliding mode control strategy for disturbed discrete time dynamical systems. The desired trajectory, which is generated externally according to an existing switching type reaching law, determines the properties of the emerging sliding motion of the system. It is proved that an appropriate choice of the trajectory generator parameters ensures the existence of the quasi-sliding motion of the system according to the definition by Gao et al. (1995) in spite of the influence of disturbances. Moreover, the paper shows that the application of the desired trajectory based reaching law results in a significant reduction in the quasi-sliding mode band width and errors of all state variables. Therefore, in comparison with Gao’s control method, the system’s robustness is increased. The paper also presents an additional modification of the reaching law, which guarantees a further reduction in the quasi-sliding mode band in the case of slowly varying disturbances. The results are confirmed with a simulation example.
7
Content available Reduced-order perfect nonlinear observers of fractional descriptor discrete-time nonlinear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2017
|
Vol. 27, no. 2
245--251
EN
The purpose of this work is to propose and characterize fractional descriptor reduced-order perfect nonlinear observers for a class of fractional descriptor discrete-time nonlinear systems. Sufficient conditions for the existence of these observers are established. The design procedure of the observers is given and demonstrated on a numerical example.
8
Content available Construction of algebraic and difference equations with a prescribed solution space
Moysis L., Karampetakis N. P.
International Journal of Applied Mathematics and Computer Science
|
2017
|
Vol. 27, no. 1
19--32
EN
This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ) β (k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ) . This work deals with the inverse problem of constructing a family of polynomial matrices A(σ) such that the system A(σ) β (k) = 0 satisfies some given forward and backward behavior. Initially, the connection between the backward behavior of an AR representation and the forward behavior of its dual system is showcased. This result is used to construct a system satisfying a certain backward behavior. By combining this result with the method provided by Gohberg et al. (2009) for constructing a system with a forward behavior, an algorithm is proposed for computing a system satisfying the prescribed forward and backward behavior.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.