Electrical and Electronic Engineering 2012, 2(3): 128-134 DOI: 10.5923/j.eee.20120203.04 New Generalized Optimization Methodology for Designing of Electronic Systems Alexander Zemliak 1,4,* , Ricardo Peña 2 , Fernando Reyes 3 , Jaime Cid 3 , Sergio Vergara 3 1 Department of Physics and Mathematics, Autonomous University of Puebla, Puebla, 72570, Mexico 2 Institute of Sciences, Autonomous University of Puebla, Puebla, 72570, Mexico 3 Department of Electronics, Autonomous University of Puebla, Puebla, 72570, Mexico 4 Institute of Physics and Technology, National Technical University of Ukraine “KPI”, Kiev, 03055, Ukraine Abstract The new general methodology for the analogue system optimization was elaborated by means of the control theory formulation in order to improve the characteristics of the process of system designing. A special vector of control is defined to redistribute the compute expense between a network analysis and a parametric optimization. This approach gen- eralizes the design process and generates a set of the different optimization strategies that serves as the structural basis to the construction of optimal designing strategy. The principal difference between this new methodology and theory that was elaborated before is the more general approach in the definition of the system parameters and more broadened structural basis. The main equations for the system optimization process have been elaborated. These equations include the special control functions that generalize the total process of optimization of system. Numerical results that include as passive and active nonlinear networks demonstrate the efficiency and perspective of the proposed approach. Keywords Network Optimization, Control Theory Approach, Optimal System Design 1. Introduction The computer time reduction for designing of large sys- tem is one of the sources of the total improvement of quality of designing. This problem has a great significance because it has a lot of applications, for example on VLSI electronic circuit design. Any traditional system design strategy in- cludes two main parts: the mathematical model of the physical system that can be defined by the algebraic or in- tegral equations and optimization procedure that achieves the optimum point of the objective function of design. There are some powerful methods that reduce the neces- sary time for the circuit analysis. Because a matrix of the large-scale circuit is a very sparse, the special sparse matrix techniques are used successfully for this purpose[1]. Other approach for reducing the amount of computational required for both linear and nonlinear equations is based on the de- composition techniques. The partitioning of a circuit matrix into bordered-block diagonal form can be done by branches tearing as in[2], or by nodes tearing as in[3] and jointly with direct solution algorithms gives the solution of the problem. The extension of the direct solution methods can be obtained by hierarchical decomposition and macromodel representa- tion [4]. Other approach for achieving decomposition at the * Corresponding author: azemliak@fcfm.buap.mx (Alexander Zemliak) Published online at http://journal.sapub.org/eee Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved nonlinear level consists on a special iteration techniques and has been realized in[5] for the iterated timing analysis and circuit simulation. Optimization technique that is used for the circuit optimization and designing gives a very strong influence on the total computer time too. The numerical methods are developed both for the unconstrained and for the constrained optimization[6] and will be improved later on. The practical aspects of these methods were developed for the electronic circuits designing with the different optimiza- tion criterions[7]. The fundamental problems of the devel- opment and adaptation of the automation designing systems were examined in some early papers[8,9]. The above described ideas of system designing can be named as the traditional approach or the traditional strategy because the method of analysis is based on the Kirchhoff laws. The other formulation of the circuit optimization problem was developed on heuristic level some decades ago[10]. This idea was based on the Kirchhoff laws ignoring for all the circuit or for the part of the circuit. The special cost function is minimized instead of the circuit equation solving. This idea was developed in practical aspect for the microwave circuit optimization[11] and for the synthesis of high- per- formance analogue circuits[12] in extremely case, when the total system model was eliminated. The authors of the last papers affirm that the designing time was reduced signifi- cantly. This last idea can be named as the modified tradi- tional design strategy. Nevertheless all these ideas can be generalized to reduce