Thevenin's Theorem, Cramer's Rule, and Parameterized Systems: Some Connections [Lecture Notes]

Engineering systems are complex systems comprising interconnections of simpler subsystems. Examples of this in electrical engineering are ac and dc circuits, motor drives, power systems, and electronic circuits. Similar examples occur in mechanical engineering, robotics, hydraulic networks, truss structures, and chemical reactors. In control engineering, complex feedback systems are created from interconnections of elementary blocks. In this article, we present a unified approach and framework applicable to the analysis of all such systems. The main unifying criterion is that the systems are described by linear equations. We show that the input-output maps of both algebraic and dynamic systems can be obtained by a common set of formulas developed by systematically applying Cramer's rule for solving linear equations.