Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a piecewise-linear resistor that is neither voltage nor current controlled. In this letter, an efficient algorithm is proposed for finding all dc operating points of piecewise-linear circuits containing such neither voltage nor current controlled resistors.

It is very difficult to obtain a linearizing feedback and a coordinate transformation map, even though the system is feedback linearizable. It is known that finding a desired transformation map and feedback is equivalent to finding an integrating factor for an annihilating one-form. In this paper we develop a numerical algorithm for an integrating factor involving a set of partial differential equations and corresponding zero-form using the C.I.R method. We employ a tensor product splines as an interpolation method to data which are resulted from the numerical algorithm in order to obtain an approximate integrating factor and a zero-form in closed forms. Next, we obtain a coordinate transformation map using the approximate integrating factor and zero-form. Finally, we construct a stabilizing controller based on a linearized system with the approximate coordinate transformation.