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1
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Separation principle for nonlinear systems: a bilinear approach

100%
Hammami M. A., Jerbi H.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 2
481-492
EN
In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i.e. the ones that make bilinear systems unobservable). A separation principle for such systems is given.
2
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Robust stabilization of discrete linear repetitive processes with switched dynamics

88%
Bochniak J., Galkowski K., Rogers E., Kummert A.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 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.
3
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Positivity and stabilization of 2D linear systems

88%
Kaczorek T.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2009
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tom 29
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nr 1
43-52
EN
The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.
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
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2010
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tom 20
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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.
5
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Local stability conditions for discrete-time cascade locally recurrent neural networks

88%
Patan K.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 1
23-34
EN
The paper deals with a specific kind of discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the network considered is a locally recurrent globally feedforward. A crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates local stability conditions for the analysed class of neural networks using Lyapunov's first method. Moreover, a stabilization problem is defined and solved as a constrained optimization task. In order to tackle this problem, a gradient projection method is adopted. The efficiency and usefulness of the proposed approach are justified by using a number of experiments.
6
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A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models

88%
Abdelmalek I., Goléa N., Hadjili M. L.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 1
39-51
EN
In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.
7
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On a criterion of D-stability for P-matrices

75%
Kushel O. Y.
Special Matrices
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2016
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tom 4
|
nr 1
181-188
EN
In this paper, we study positive stability and D-stability of P-matrices.We introduce the property of Dθ-stability, i.e., the stability with respect to a given order θ. For an n × n P-matrix A, we prove a new criterion of D-stability and Dθ-stability, based on the properties of matrix scalings.
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