A method for the formulation and solution of circuits composed of switches and linear RLC elements

Abstract

Networks composed of switches <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(S)</tex> and linear RLC elements are formulated by state-space equations in which the switches <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</tex> are dealt with as the voltage sources <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_s ( = 0)</tex> for closed switches and current sources <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i_s ( = 0)</tex> for open switches. The equation associated with the change of switching combinations (mode change) is modified. The solution of the jump of the state vector which occurs at mode change is made clear in the distribution sense. The invariance of state space under mode change is discussed, and the concept of switch controllability and observability is introduced to solve this problem.