Advanced algorithm for stability analysis of combined dynamical systems

A hybrid dynamical system (HDS) is a system of ordinary and partial differential equations under some boundary conditions, constraints, and initial conditions. A “fast” algorithm for analyzing the stability of an HDS is applicable only in the case where the characteristic and perturbing quasipolynomials are analytic to the right of the imaginary axis and in its neighborhood. We propose an advanced algorithm for analyzing the stability of an HDS, which is free from this restriction, and compare its complexity with the “fast” algorithm.