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

One of the world’s prime difficulties within the box of nationwide safety is defense of borders and borderlands. This publication addresses a number of concerns on complex cutting edge equipment of multi-level regulate of either flooring (UGVs) and aerial drones (UAVs). these gadgets mixed with leading edge algorithms develop into self sufficient gadgets in a position to patrolling selected borderland components by way of themselves and immediately tell the operator of the method approximately capability position of detection of a particular incident. this can be completed through the use of sophisticated

methods of iteration of non-collision trajectory for these sorts of items and allowing computerized integration of either floor and aerial unmanned cars.

The subject matters incorporated during this ebook additionally conceal presentation of whole info and conversation expertise (ICT) structures able to regulate, commentary and detection of assorted kinds of incidents and threats. This booklet is a necessary resource of knowledge for constructors and builders of such ideas for uniformed providers. Scientists and researchers eager about machine imaginative and prescient, photograph processing, facts fusion, keep an eye on algorithms or IC can locate many worthy feedback and suggestions. a number of demanding situations for such platforms also are awarded.

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**Extra resources for Advanced Technologies for Intelligent Systems of National Border Security**

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Petersburg University. Mathematics 39(2), 55–63 (2005) 38. : Stability Criteria by the First Approximation for Discrete Nonlinear Systems (part II), Vestnik St. Petersburg University. Mathematics 39(3), 30– 42 (2005) 39. : Exact Lyapunov exponent for infinite products of random matrices. Journal of Physics A: Mathematical and General 27(10), 3427–3437 (1994) 40. : General problem of stability of motion, Collected works. Izdat. Akad. Nauk SSSR 2 (1956) (in Russian) 41. : Lyapunov exponents and problems of linearization.

The next Theorem contains the main result of this section. Theorem 16. If λ (Δ ) < −σG , (31) then the spectra of (1) and (6) coincide. As it is shown in the next theorem, in case of diagonal matrices A(n), spectra of (1) and (6) coincide for perturbations with characteristic exponent equal to −σG . Theorem 17. If the matrices A(n) are diagonal and λ (Δ ) ≤ −σG < 0, (32) then the spectra of (1) and (6) coincide. Together with (1) consider the following non-homogeneous system x(n + 1) = A(n)x(n) + f (n), (33) where the sequence f = ( f (n))n∈N belongs to the class F consisting of all sequences g of s-dimensional vectors such that 42 A.

For a initial condition x(0) = x0 ∈ Rs the solution of (1) is denoted by x(n, x0 ), so x(n, x0 ) = A (n, 0)x0 . Definition 1. Let b = (b(n))n∈N be a sequence of real numbers. 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 .