Stability of analogue circuit optimization process and control vector structure


  • A. M. Zemliak Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine; Autonomous University of Puebla
  • Tatiana Markina National Technical University of Ukraine "Kyiv Polytechnic Institute"



optimal designing of circuits, strategy of optimization, control theory, stability, Lyapunov function


Analogue circuit optimization process may be controlled using a generalized design methodology. Lyapunov function is an integral function that carries information on this process. The use of Lyapunov function concept for a dynamic system allowed for comparison of various design strategies with respect to their stability and convergence. Study of Lyapunov function’s and its derivative’s behavior allowed for revealing significant correlation between this function’s properties and processor time for circuit design. Analysis of processor time dependence on control vector switching points provided a possibility to find this vector’s optimal structure. Numerical results prove bright future of such approach for finding quasi-optimal algorithm of analogue circuits design.


ZEMLIAK, A.M. Analog system design problem formulation by optimum control theory. IEICE Trans. Fund. Elec., Commun. Computer Sci., v.E84-A, n.8, p.2029-2041, 2001.

ZEMLIAK, A.M. Analogue circuits design using control theory methods. I. Theory. Radioelectron. Commun. Syst., v.47, n.5, p.14, 2004.

ZEMLIAK, A. Analysis of the Lyapunov function characteristics for the minimal-time design strategy. WSEAS Trans. Circuits Syst., v.6, n.1, p.110-116, 2007.

ZEMLIAK, A.M. Analogue circuits design using control theory methods. II. Numerical results. Radioelectron. Commun. Syst., v.47, n.6, p.55, 2004.

BARBASHIN, YE.A. Introduction to Stability Theory. Moscow: Nauka, 1967. 223 p. [in Russian].

ROUCHE, N.; HABETS, P.; LALOY, M. Stability Theory by Liapunov’s Direct Method. New York: Springer-Verlag, 1977. 222 p.





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