Second-order numerator-dynamics systems: Effects of initial discontinuities

Linear second-order systems with numerator-dynamics are considered and their transient responses are investigated for discontinuous inputs. Characteristic parameters for second-order systems with numerator dynamics are identified. The solution profiles of these systems depend upon the value of one such parameter relative to that of the others on the number line. Effects of initial jump discontinuities of the inputs on the correctness of the solutions are also treated. A methodology for analysis of discontinuities is presented. Initial discontinuities of the calculated response either get accounted for in the input function or the initial condition of the input function for all but the following case. For the impulse response alone, that too among inherent numerator-dynamics systems only, an initial di scontinuity cannot be accounted for in the input. The value of that discontinuity is thus required for correct solutions of these cases. The results are general and extendable to different inputs and higher order systems.