Cone-Copositive Lyapunov Functions for Complementarity Systems: Converse Result and Polynomial Approximation

This article establishes the existence of Lyapunov functions for analyzing stability a class state-constrained systems, and it describes algorithms their numerical computation. The system model consists differential equation coupled with set-valued relation which introduces discontinuities in vector field at boundaries constraint set. In particular, is described by subdifferential indicator function closed convex cone, results cone-complementarity system. question such systems addressed constructing cone-copositive functions. As first analytical result, we show that exponentially stable complementarity always admit continuously differentiable function. Putting some more structure on field, as homogeneity, can aforementioned be approximated rational homogeneous polynomials. later seen to particularly amenable computation provide two types precisely purpose. These consist hierarchy either linear or semidefinite optimization problems computing desired Some examples are given illustrate our approach.