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1
Content available remote

An observability problem for a class of uncertain-parameter linear dynamic systems

100%
Oprzędkiewicz K.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 3
331-338
EN
An observability problem for a class of linear, uncertain-parameter, time-invariant dynamic SISO systems is discussed. The class of systems under consideration is described by a finite dimensional state-space equation with an interval diagonal state matrix, known control and output matrices and a two-dimensional uncertain parameter space. For the system considered a simple geometric interpretation of the system spectrum can be given. The geometric interpretation of the system spectrum is the base for defining observability and non-observability areas for the discussed system. The duality principle allows us to test observablity using controllability criteria. For the uncertain-parameter system considered, some controllability criteria presented in the author's previous papers are used. The results are illustrated with numerical examples.
2
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Regional boundary observability: a numerical approach

80%
Zerrik E. H., Bourray H., Boutoulout A.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 2
143-151
EN
In this paper we review the concept of regional boundary observability, developed in (Michelitti, 1976), by means of sensor structures. This leads to the so-called boundary strategic sensors. A characterization of such sensors which guarantees regional boundary observability is given. The results obtained are applied to a two-dimensional system, and various cases of sensors are considered. We also describe an approach which leads to the estimation of the initial boundary state, which is illustrated by simulations.
3
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Positive 2D discrete-time linear Lyapunov systems

80%
Przyborowski P., Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 1
95-105
EN
Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
4
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Regional observation and sensors

80%
El Jai A., Hamzaoui H.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 1
5-14
EN
The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.
5
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Gradient observability for diffusion systems

70%
Zerrik E. H., Bourray H.
International Journal of Applied Mathematics and Computer Science
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2003
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tom 13
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nr 2
139-150
EN
The aim of this paper is to study regional gradient observability for a diffusion system and the reconstruction of the state gradient without the knowledge of the state. First, we give definitions and characterizations of these new concepts and establish necessary conditions for the sensor structure in order to obtain regional gradient observability. We also explore an approach which allows for a regional gradient reconstruction. The developed method is original and leads to a numerical algorithm illustrated by simulations.
6
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An approach to the analysis of observability and controllability in nonlinear systems via linear methods

70%
Zhirabok A., Shumsky A.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 3
507-522
EN
The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g., Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.
7
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Controllability, observability and optimal control of continuous-time 2-D systems

70%
Jank G.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 2
181-195
EN
We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data. The optimal control problem with a quadratic cost functional is also solved.
8
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Controllability and observability of linear discrete-time fractional-order systems

61%
Guermah S., Djennoune S., Bettayeb M.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 2
213-222
EN
In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.
9
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Continuity of solutions of Riccati equations for the discrete-time JLQP

61%
Czornik A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 4
539-543
EN
The continuity of the solutions of difference and algebraic coupled Riccati equations for the discrete-time Markovian jump linear quadratic control problem as a function of coefficients is verified. The line of reasoning goes through the use of the minimum property formulated analogously to the one for coupled continuous Riccati equations presented by Wonham and a set of comparison theorems.
10
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Observability and controllability analysis for sandwich systems with backlash

61%
Luo N., Tan Y., Dong R.
International Journal of Applied Mathematics and Computer Science
|
2015
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tom 25
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nr 4
803-814
EN
In this paper, an approach to analyze the observability and controllability of sandwich systems with backlash is proposed. In this method, a non-smooth state-space function is used to describe the sandwich systems with backlash which are also non-smooth non-linear systems. Then, a linearization method based on non-smooth optimization is proposed to derive a linearized state-space function to approximate the non-smooth sandwich systems within a bounded region around the equilibrium point that we are interested in. Afterwards, both observability and controllability matrices are constructed and the methods to analyze the observability as well as controllability of sandwich system with backlash are derived. Finally, numerical examples are presented to validate the proposed method.
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