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1
Content available Results on the controllability of Caputo’s fractional descriptor systems with constant delays
Beata Sikora
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2023
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Vol. 71, nr 4
art. no. e146287
EN
The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
2
Content available Generalized observer design of index one for descriptor systems with unknown inputs
Kumar Abhinav, Gupta Mahendra Kumar
Archives of Control Sciences
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2023
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Vol. 33, No. 1
83--99
EN
Generalized observers are proposed to relax the existing conditions required to design Luenberger observers for rectangular linear descriptor systems with unknown inputs. The current work is focused on designing index one generalized observers, which can be naturally extended to higher indexes. Sufficient conditions in terms of system operators for the existence of generalized observers are given and proved. Orthogonal transformations are used to derive the results. A physical model is presented to show the usefulness of the proposed theory.
3
Content available Nonnegativity, stability analysis of linear discrete-time positive descriptor systems: an optimization approach
Yang H., Zhou M., Zhao M., Pan P.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2018
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Vol. 66, nr 1
1--7
EN
This paper discusses an efficient approach to the analysis of positivity and stability of linear discrete-time positive descriptor system. Irs main objective is to convert the necessary and sufficient condition of characterizing positivity and stability of positive descriptor systems into an optimization problem, then propose a method to numerically check the positivity and stability of the positive linear discrete-time systems. Comparing with the other methods now available, the approach presented in this paper is less theoretical and easier to implement. Examples are provided in order to validate results.
4
Content available Disturbance attenuation problem using a differential game approach for feedback linear quadratic descriptor systems
Musthofa M. W.
Archives of Control Sciences
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2015
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Vol. 25, no. 4
445--462
EN
This paper studies the H∞ disturbance attenuation problem for index one descriptor systems using the theory of differential games. To solve this disturbance attenuation problem the problem is converted into a reduced ordinary zero-sum game. Within a linear quadratic setting the problem is solved for feedback information structure.
5
Content available Feedback saddle point equilibria for soft-constrained zero-sum linear quadratic descriptor differential game
Musthofa M. W., Salmah, Engwerda J. C., Suparwanto A
Archives of Control Sciences
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2013
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Vol. 23, no. 4
473--493
EN
In this paper the feedback saddle point equilibria of soft-constrained zero-sum linear quadratic differential games for descriptor systems that have index one will be studied for a finite and infinite planning horizon. Both necessary and sufficient conditions for the existence of a feedback saddle point equilibrium are considered.
6
A class of LTI descriptor (regular) differential systems with distributed continuous delays and several types of inputs
Pantelous A. A., Kalogeropoulos G. I.
Systems Science
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2009
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Vol. 35, no 1
31-38
EN
In this paper, we consider a class of Linear Time-Invariant (LTI) descriptor (regular) differential systems with distributed continuous delays and several types of (regular and irregular) inputs. This special class of differential systems are inherent in many real-life applications; we merely mention fluid dynamics, the modelling of multi-body mechanisms, the pricing procedure of actuarial portfolios of products and the problem of protein folding. By using some elements of matrix pencil theory, we decompose the main system into two subsystems (which are so-called fast and slow systems), whose solutions are obtained as generalized processes (in the sense of the Dirac delta distributions). Moreover, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable. Finally, an illustrative application inspired by Insurance is briefly presented using standard Brownian motions.
7
Content available Modelling and control of mechatronic systems by the descriptor approach
Muller P. C.
Journal of Theoretical and Applied Mechanics
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2005
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Vol. 43 nr 3
593--607
EN
In recent years, the analysis and synthesis of control systems in a descriptor form has been established. The general description of dynamical systems by differential-algebraic equations (DAE) is important for many applications in various disciplines, but particularly in mechatronics. In this contribution, the pros and cons of the modelling of mechatronic systems by differential-algebraic equations are discussed with application of subsystem modelling. Additionally, the actual state of the art simulation, analysis and design of descriptor systems are presented.
PL
W ostatnich latach sformułowano i spopularyzowano problem analizy i syntezy układów sterujących w postaci deskrypcyjnej. Ogólny opis układów dynamicznych za pomocą równań różniczkowo-algebraicznych (DAE) ma ogromne znaczenie aplikacyjne w różnych dziedzinach nauki, w szczególności w zakresie mechatroniki. W prezentowanej pracy przedyskutowano wszystkie "za" i "przeciw" modelowania układów mechatronicznych równaniami różniczkowo-algebraicznymi z zastosowaniem podziału opisywanego układu na podsystemy. Ponadto przedstawiono najnowocześniejsze metody symulacji, analizy i projektowania układów deskrypcyjnych.
8
Content available remote Computing Generalized Inverse Systems Using Matrix Pencil Methods
Varga A.
International Journal of Applied Mathematics and Computer Science
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2001
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Vol. 11, no 5
1055-1068
EN
We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil to appropriate Kronecker-like forms.
9
Content available remote Stability and optimal control of nonlinear descriptor systems: a survey
Müller P. C.
Applied Mathematics and Computer Science
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1998
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Vol. 8, no 2
269-286
EN
In recent years the analysis and synthesis of contral systems in descriptor form have been established. This general description of dynamical systems is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. This contribution presents a survey of results on the stability analysis and on the optimal control design of such systems. Lyapunov's stability theory is generalized for descriptor systems based on the stability theory with respect to a part of variables. Similarly, the calculus of variations and Pontryagin's maximum principle are checked for a possible application in descriptor systems. Here, the notion of causality plays an important role in whether or not Pontryagin's maximum principle can be applied.
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