Paper detail

Transverse Dynamics and Regions of Stability for Nonlinear Hybrid Limit Cycles

This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from the linearization of the transverse dynamics construct a quadratic candidate Lyapunov function; (3) search for a new Lyapunov function verifying maximal regions of orbital stability via iterated of sum-of-squares programs. The construction of the transverse dynamics is novel, and valid for a broad class of nonlinear hybrid systems. The problem of stabilization of unstable limit cycles will also be addressed, and a solution given based on stabilization of the transverse linearization.