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EN
This paper focuses on the invariance of the reachability and observability for fractional order positive linear electrical circuits with delays and their checking methods. By derivation and comparison, it shows that conditions and checking methods of reachability and observability for integer and fractional order positive linear electrical circuits with delays are invariant. An illustrative example is presented at the end of the paper.
EN
The invariant properties of the stability, reachability, and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
EN
In this paper we extend the method of obtaining symmetries of ordinary differential equations to first order non-homogeneous neutral differential equations with variable coefficients. The existing method for delay differential equations uses a Lie-Bäcklund operator and an Invariant Manifold Theorem to define the operators which are used to obtain the infinitesimal generators of the Lie group. In this paper, we adopt a different approach and use Taylor’s theorem to obtain a Lie type invariance condition and the determining equations for a neutral differential equation. We then split this equation in a manner similar to that of ordinary differential equations to obtain an over-determined system of partial differential equations. These equations are then solved to obtain corresponding infinitesimals, and hence desired equivalent symmetries. We then obtain the symmetry algebra admitted by this neutral differential equation.
EN
The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
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EN
Inspired by the recent results of A.E. Abbas we determine continuous multivariate utility functions invariant with respect to a wide family of transformations related to the shift transformations.
EN
Inspired by some relevant recent results of A. E. Abbas we determine utility functions invariant with respect to some classes of transformations.
7
Content available remote On stability in impulsive dynamical systems
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.
8
Content available remote On an invariant Borel measure in Hilbert space
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].
EN
A method of fault isolation in a given concurrent system is presented. First, the system considered is modelled by a live and bounded place-transition Petri net. Then the corresponding net place invariants are computed. The system k-distinguishability measure is obtained in an unique way from the place-invariant matrix. For a large value of k, the system model is extended by using some set of additional places called test points. This is in accordance with the practical requirements introduced. To obtain an 1-distinguishable net the notion of a marked graph component is used. Next, two different diagnosis test strategies are discussed, i.e., combinational and sequential fault diagnosis (assuming MTBF -> infinity and MTTR -> 0, respectively). The approach proposed can be extended for higher level Petri nets, e.g., such as coloured nets or also to design self-diagnosable circuit realisations of Boolean interpreted Petri nets. Several examples are given.
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.
11
Content available remote On invariance of linear subspaces for stochastic evolution equations
EN
In the paper we consider Ito equation on a Hilbert space. We give necessary and sufficient conditions ensuring the invariance property of linear subspaces of the state space by mild solutions to the equation.
12
Content available remote Reachability and Controlability of Positive Linear Systems with State Feedbacks
EN
It is shown that the reachability and controllability of positive linear systems is not invariant under the state-feedbacks.
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