Advanced Technologies for Intelligent Systems of National by Zygmunt Kuś, Sławomir Fraś (auth.), Aleksander Nawrat,

By Zygmunt Kuś, Sławomir Fraś (auth.), Aleksander Nawrat, Krzysztof Simek, Andrzej Świerniak (eds.)

One of the world’s major difficulties within the box of nationwide protection is safeguard of borders and borderlands. This ebook addresses a number of concerns on complex leading edge equipment of multi-level keep an eye on of either flooring (UGVs) and aerial drones (UAVs). these items mixed with leading edge algorithms turn into independent items able to patrolling selected borderland components by means of themselves and instantly tell the operator of the approach approximately power position of detection of a selected incident. this is often completed through the use of sophisticated

methods of new release of non-collision trajectory for these forms of gadgets and permitting computerized integration of either floor and aerial unmanned cars.

The subject matters integrated during this e-book additionally conceal presentation of entire info and communique know-how (ICT) platforms able to keep watch over, commentary and detection of varied sorts of incidents and threats. This booklet is a worthwhile resource of data for constructors and builders of such options for uniformed companies. Scientists and researchers enthusiastic about desktop imaginative and prescient, snapshot processing, info fusion, keep watch over algorithms or IC can locate many useful feedback and ideas. a number of demanding situations for such structures also are provided.

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Exponential Stability by the Linear Approximation. Differential Equations 37(8) (2001) 30. : The Higher Exponent of a Linear System with Exponential Perturbations. Differential Equations 5(7), 1186–1192 (1969) 31. : The Higher Exponent of a System with Perturbations of Order Higher Than One. Vestn. Bel. Gos. Unta. Ser. I (3), 6–9 (1969) (in Russian) 32. : Vvedenie v teoriyu pokazatelei Lyapunova (Introduction to the Theory of Lyapunov Exponents). Belarus. Gos. , Minsk (2006) (in Russian) 33. : Robustness of a discrete system.

Xl are linearly independent; 5. , xs is a basis or Rs then s 1 lim sup ln |detA (n, 0)| ≤ ∑ λA (xl ) ; n→∞ n l=1 (3) 6. if x0 ∈ Rs then λA (x0 ) ≤ a; 7. if x0 ∈ Rs then λA (s) ≤ λA (x0 ), where v = (v(n))n∈N is given by v(n) = ∑n−1 l=0 x(l, x0 ) if λ (x0 ) ≥ 0 . 1, inequality (3), which is called Lyapunov inequality was shown in [22], point 6 is a obvious consequence of (2) and the definition of λA (x0 ), point 7 is proved in [16], Lemma 4. As a consequence 32 A. Czornik, A. Nawrat, and M. Niezabitowski of point 4 we see that the set {λA (x0 ) : x0 ∈ Rs \ {0}} contains at most s elements, say −∞ ≤ λ1 (A) < λ2 (A) < ...

The number (or the symbol ±∞) defined as 1 λ (b) = lim sup ln |b(n)| n→∞ n is called the upper characteristic exponent or simply characteristic exponent of sequence (b(n))n∈N . For a sequence v = (v(n))n∈N of vectors of normed space (X, ∗ ) we define its characteristic exponent λ (v) as a exponent of sequence ( v(n) )n∈N . It is easy to check that finite λ (b) is a characteristic exponent of sequence of b = (b(n))n∈N if, and only if, the following two conditions are simultaneously satisfied: 1.

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