By G. Rega, F. Vestroni
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13] C. Wu, Y. Yang, and L. Chua, “On adaptive synchronisation and control of nonlinear dynamical systems,” Intern. J. of Bifurcation and Chaos, 6, pp. 455–471, 1996.  S. S. Ge and C. Wang, “Adaptive control of uncertain Chua circuits,” IEEE Trans. on Circuit and Systems-I, 47, 9, pp. 1397–1402, 2000.  H. Huijberts, H. Nijmeijer, and R. Willems, “System identification in communication with chaotic systems,” IEEE Trans. on Circuit and Systems-I, 47, 6, pp. 800–808, 2000.  A. L. Fradkov, V.
10) Hence, according to previous discussion, signal / is bounded and signal &/ is ultimately bounded. Let us analyze the following Lyapunov function candidate with respect to part of variables  : ( )= γ − ( − ) ( − ) , its time derivative for system (8) takes form: 7 : = − ( − ) ≤− & 7 − 7 7 ( ( − ))≤ & & /+ + &/ = − γ & : + & / According to Lemma 1 solution of the last linear time-varying inequality is bounded, if functions γ & ( W ) and &/( W ) are.
This speculative model may provide a paradigm for the role of nonlinear dynamics and chaotic noise in the design evolution of machines. 5. References  H. G. Conway, “Origins of mechanical servo mechanisms”, The Newcomen Society, Vol. XXIX, 1953-54, 1954-55.  F. C. Moon, Chaotic and Fractal Dynamics, J. Wiley, New York, 1992.  F. Reuleaux, The Constructor, 4th Edition, Translated by H. Suplee, 1893.  C. Huygens, Horologium, 1658.  D. Sobel and W. J. H. Y, 1998.  G. B. Airy, (1826) “On the disturbances of pendulums and balances and the theory of escapements”, Trans.