Rigorous Verification of Poincaré Map Generated by a Continuous Piece-Wise Linear Vector Field and Its Application

This paper provides algorithms in order to solve an interval implicit function of the Poincaré map generated by a continuous piecewise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MAT LAB and INT LAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective. key words: interval arithmetic, computer assisted rigorous proof, Poincaré map, canard, slow-fast system, continuous piece-wise linear vector field