[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

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Estimation of Solution of Discrete Linear Time-Varying System 325 3 Conclusion In this paper we have obtained upper and lower bounds for norm of solution of linear discrete time-varying system in terms of coefficients of matrices A(n). Itis interesting that to calculate our bounds we do not need to know eigenvalues or spectral norm of matrices because we can simply calculate it by matrix coefficients. It is also worth to notice that our bounds are also valid in case of singular matrices. Moreover, in the paper, as the corollary of our results, we have obtained an upper estimate for stationary system. Presented solutions can be widely used in the algorithms of data transmission [19], [20] and control developed by the research team from Silesian University of Technology. The proposed method can be particularly useful for high-compression algorithms where the key parameter is the time of computation. A time series analysis can bring a significant increase of efficiency of the communication system between the UAV and mobile control station. The presented methods could also be used for communication channel modeling applications. In particular important is the ability to apply to applications related to cryptography and signal variability analysis and validation of quality of encryption algorithms. Acknowledgements. The research presented here was done by first author as a part of the project funded by the National Science Centre granted according to decision DEC- 2012/05/B/ST7/ 00065. The research of the second author was co-financed by the European Union within European Social Fund for SWIFT project POKL. 08.02.01-24-005/10. References 1. Adrianova, L.Y.: Introduction to Linear Systems of Differential Equations, vol. 146. AMS Bookstore (1995) 2. Arnold, L., Crauel, H., Eckmann, J.P. (eds.): Lyapunov Exponents. Proceedings of a Conference, held in Oberwolfach, May 28-June 2. Lecture Notes in Mathematics, vol. 1486. Springer, Berlin (1991) 3. Awad, L.R., El-Kholy, E.M., El-Bendary, S.: On the Estimation of Solutions for Some Linear Systems of Differential Equations. Acta Mathematica Sinica, New Series 14(1), 41–46 (1998) 4. Barreira, L., Pesin, Y.: Lyapunov exponents and Smooth Ergodic Theory. Univ. Lecture Ser., vol, 23. Amer. Math Soc., Providence (2002) 5. Li, C., Chen, G.: Estimating the Lyapunov exponents of discrete systems. Chaos 14(2), 343–346 (2004) 6. Li, C., Xia, X.: On the bound of the Lyapunov exponents for continuous systems. Chaos 14(3), 557–561 (2004) 7. Czornik, A., Jurgas, P.: Set of possible values ofmaximal Lyapunov exponents of discrete time-varying linear system. Automatica 44(2), 580–583 (2008) 8. Czornik, A., Nawrat, A.: On new estimates for Lyapunov exponents of discrete timevarying linear systems. Automatica 46(4), 775–778 (2010)
326 A. Czornik, A. Nawrat, and M. Niezabitowski 9. Czornik, A.: Bounds for characteristic exponents of discrete linear time-varying systems. Journal of the Franklin Institute-Engineering and Applied Mathematics 347(2), 502–507 (2010) 10. Czornik, A., Mokry, P., Niezabitowski, M.: On a Continuity of characteristic exponents of linear discrete time-varying systems. Archives of Control Sciences 22(LVIII), 17–27 (2012) 11. Czornik, A., Niezabitowski, M.: O parametrycznej zale żności wykładników Lapunowa dyskretnych układów liniowych. In: XVIII Krajowa Konferencja Automatyzacji Procesów Dyskretnych w Zakopanem September 19-22, Analiza procesów dyskretnych, Tom I, pp. 41–48 (2012) 12. Czornik, A., Niezabitowski, M.: Lyapunov Exponents for Systems with Unbounded Coefficients. - To appear in Dynamical Systems: An International Journal (2012) 13. Czornik, A., Nawrat, A., Niezabitowski, M.: On the Lyapunov exponents of a class of the second order discrete time linear systems with bounded perturbations. - To appear in Dynamical Systems: An International Journal (2012) 14. Key, E.S.: Lower bounds for the maximal Lyapunov exponent. Journal of Theoretical Probability 3(3), 477–487 (1990) 15. Leonov, G.A.: Strange Attractors and Classical Stability Theory. Nonlinear Dynamics and Systems Theory 8(1), 49–96 (2008) 16. Leonov, G.A.: Strange Attractors and Classical Stability Theory. St. Petersburg University Press (2009) 17. Rudin, W.: Real and Complex Analysis, 3rd edn. McGraw Hill, Boston (1987) 18. Smith, R.A.: Bounds for the characteristic exponents of linear systems. Proc. Camb. Phil. Soc. 61, 889–894 (1965) 19. Topór-Kamiński, T., Żurkowski, R., Grygiel, M.: Selected methods of measuring the delay in data transmission systems with wireless network interfaces. Acta Phys. Pol. A 120(4), 748–754 (2011) 20. Topór-Kamiñski, T., Krupanek, B., Homa, J.: Delays models of measurement and control data transmission network. In: Nawrat, A., Simek, K., Świerniak, A. (eds.) Advanced Technologies for Intelligent Systems of National Border Security. SCI, vol. 440, pp. 257–278. Springer, Heidelberg (2013)
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Studies in Computational Intelligen
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Aleksander Nawrat · Zygmunt Kuś E
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“In God We Trust, All others we o
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VIII Preface valuable information i
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Contents Part I: Design of Object D
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Contents XIII Technology Developmen
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XVI List of Contributors Adam Czorn
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XVIII List of Contributors Henryk M
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XX List of Contributors Józef Wron
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2 Design of Object Detection, Recog
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4 A. Babiarz et al. 1 Introduction
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6 A. Babiarz et al. The description
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Recognition and Location of Objects
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Omnidirectional Video Acquisition D
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[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

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