2019/09/16 by Sajeev Ahuja, Ahuja, Sajeev, Raj Kumar Arya +1
Decision Sciences · Engineering · #FOS: Electrical engineering #Heat Transfer and Numerical Methods #Physics and Engineering Research Articles #Scientific Measurement and Uncertainty Evaluation #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1909.07813
openalex publication_date 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consistent initialization of the Laplace transform has been a fundamental and long-standing issue. The consistency of the L- approach has been questioned, yet it is a popular approach since the L+ approach requires a priori computation of the 0+ initial conditions, which becomes a diligent task from the available methods. Also, the L+ Laplace transform of the impulse becomes zero, thus involving an inconsistency. In contrast to these direct approaches, some studies propose convoluted methods to address the issue. Here, a direct, facile, and first-principles novel approach for the L+ transform is proposed. It computes the consistent 0+ initial conditions and solution based on singular-nonsingular decomposition of the system model. The inconsistency associated with the L+ Laplace transform of discontinuous functions and impulse is not involved in the nonsingular part. The emergence of discontinuity is easily elucidated from the singular part, and the solution yields the same 0+ initial values as the initial conditions used. Further, physical first-principles can be used in the midst of the computation to validate the results to ensure error-free execution.