Jacobian pattern synthesis and application for dynamic system ensembles using boolean linear fraction transformation

Simulation and analysis of complex, large-scale dynamic systems can be challenging. Complex system structures are difficult for systems engineers to explore and comprehend, and simulating large-scale systems often requires long computation time because of the size of the system equations. This paper introduces the Jacobian pattern for continuous dynamic systems. A Boolean linear fractional transformation (BLFT) computation is developed to compute the Jacobian pattern for a block diagram model by extending the existing Jacobian accumulation algorithm in the modeling and simulation environment Simulink. Applications illustrate faster simulation as well as the ability to better analyze and comprehend how variables on a dynamic system model affect one another.