78e8a8f8-a4cd-4b79-bb99-c057f6085d2020210322061416032wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS1109-277710.37394/23202http://wseas.org/wseas/cms.action?id=4067220202022020201910.37394/23202.2020.19http://wseas.org/wseas/cms.action?id=23194AlexanderZemliakDepartment of Physics and Mathematics, Autonomous University of Puebla, Puebla, Mexico, also with Institute of Physics and Technology, National Technical University of Ukraine, UKRAINEThe process of optimizing the circuit is formulated as a controlled dynamic system. A special control vector has been defined to redistribute the computational cost between circuit analysis and parametric optimization. This redistribution will help solve the task of optimizing the circuit for minimum CPU time. In this case, the task of optimizing the circuit with minimal CPU time can be formulated as the classical optimal control problem for minimizing some functional. The concept of the Lyapunov function of a controlled dynamic system is used to analyze the main characteristics of the design process. An analysis of the Lyapunov function and its time derivative makes it possible to predict the optimal structure of the control vector for constructing an optimal or quasi-optimal circuit design algorithm. The results are based on the previously discovered effect of accelerating the design process. In this case, the optimal structure of the control vector is determined, which minimizes processor time.41020204102020107114https://www.wseas.org/multimedia/journals/systems/2020/a305103-052.pdf10.37394/23202.2020.19.15http://www.wseas.org/multimedia/journals/systems/2020/a305103-052.pdfJ.R. Bunch and D.J. Rose, (Eds.), Sparse Matrix Computations, Acad. Press, N.Y., 1976. O. Osterby and Z. Zlatev, Direct Methods for Sparse Matrices, Springer-Verlag, N.Y., 1983. 10.1109/tcs.1976.1084166F.F. Wu, Solution of Large-Scale Networks by Tearing, IEEE Trans. Circuits Syst., Vol. CAS-23, No. 12, 1976, pp. 706-713. 10.1109/tcs.1977.1084298A. Sangiovanni-Vincentelli, L.K. Chen and L.O. Chua, An Efficient Cluster Algorithm for Tearing Large-Scale Networks, IEEE Trans. Circuits Syst., Vol. CAS-24, No. 12, 1977, pp. 709-717. N. Rabat, A.E. Ruehli, G.W. Mahoney and J.J. Coleman, A Survey of Macromodeling, Proc. of the IEEE Int. Symp. Circuits Systems, April, 1985, pp. 139-143. I.S. Kashirskiy and I.K. Trokhimenko, General Optimization for Electronic Circuits, Tekhnika, Kiev, 1979. 10.1109/mwsym.1990.99588V. Rizzoli, A. Costanzo and C. Cecchetti, Numerical optimization of broadband nonlinear microwave circuits, IEEE MTT-S Int. Symp., Vol. 1, 1990, pp. 335-338. 10.1109/43.489099E.S. Ochotta, R.A.Rutenbar and L.R. Carley, Synthesis of High-Performance Analog Circuits in ASTRX/OBLX, IEEE Trans. on CAD, Vol.15, No. 3, 1996, pp. 273-294.A.M. Zemliak, Design of Analog Networks by Control Theory Methods, Part 1, Theory, Radioelectronics and Communications Systems, Vol. 47, No. 5, 2004, pp. 11-17. 10.1108/compel-10-2013-0324A. Zemliak, Analog circuit optimization on basis of control theory approach, COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 33, No. 6, 2014. pp. 2180-2204. A.M. Zemliak, Acceleration Effect of System Design Process, IEICE Trans. on Fundam., Vol. E85-A, No. 7, 2002, pp. 1751-1759. E.A. Barbashin, Introduction to the Stability Theory, Nauka, Moscow, 1967. 10.1007/978-1-4684-9362-7_1N. Rouche, P. Habets and M. Laloy, Stability Theory by Liapunov’s Direct Method, Springer-Verlag, N.Y, 1977. 10.3103/s0735272707110039A.M. Zemliak, Analysis of Dynamic Characteristics of Process of Designing Analogue Circuits, Radioelectronics and Communications Systems, Vol. 50, No. 11, 2007, pp. 603-608. A. Zemliak, T Markina, Behaviour of Lyapunov ́s function for different strategies of circuit optimization, International Journal of Electronics, Vol. 102, No. 4, 2015, pp. 619-634. G. Massobrio G. and P. Antognetti, Semiconductor Device Modeling with SPICE, N.Y.: Mc. Graw-Hill, Inc., 1993.