Modeling and sensitivity analysis methodology for hybrid dynamical systems

This paper provides an analytical methodology to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) system. The hybrid ODE system is characterized by discontinuities in the velocity state variables due to an impulsive jump caused by an instantaneous impact in the motion of the system. The analytical methodology that solves this problem is structured based on jumping conditions for both the state variables and the sensitivities matrix. The proposed analytical approach is of the benchmarked against a numerical method.