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1

Variable structure observer design for a class of uncertain systems with a time-varying delay

Liu W. J. W. J.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 3

575-583

EN

Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.

2

On stability in impulsive dynamical systems

Ciesielski K.

Bulletin of the Polish Academy of Sciences. Mathematics

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2004

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Vol. 52, nr 1

81-91

EN

Several results on stability in impulsive dynamical systems are proved. The first main result gives equivalent conditions for stability of a compact set. In particular, a generalization of Ura's theorem to the case of impulsive systems is shown. The second main theorem says that under some additional assumptions every component of a stable set is stable. Also, several examples indicating possible complicated phenomena in impulsive systems are presented.

3

On an invariant Borel measure in Hilbert space

Pantsulaia G.

Bulletin of the Polish Academy of Sciences. Mathematics

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2004

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Vol. 52, nr 1

47-51

EN

An example of a nonzero [sigma]-finite Borel measure [my] with everywhere dense linear manifold I[my] of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space l[2] such that [my] and any shift [my]^[alpha] of [my] by a vector [alpha] is an element of l[2] \ I[my] are neither equivalent nor orthogonal. This extends a result established in [7].

4

Improvement and invariance analysis of Zernike moments using as a region-based shape descriptor

Ye B., Peng J.

Image Processing & Communications

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2002

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Vol. 8, no 3

11-20

EN

In order to retrieve an image from a large image database, the descriptor should be invariant to scale and rotation. It must, also have enough discriminating power and immunity to noise for retrieval from a large image database. The Zernike moment descriptor has manv desirable properties such as rotation invariance, robustness to noise, expression efficiency, fast computation and multi-level representation for describing the shapes of patterns, but it does not possess scale invariance. In this paper, we present an improved Zernike moment descriptor that not only has rotation invariance, but also has scale invariance. We apply the improved Zernike moments to image recognition using as an elective descriptor of global shape of an image in a large image database. The experimemtal results show that the improved Zernike moment has better invariant properties than unimproved Zernike moment using as region-based shape descriptor.