Two extended abstracts submitted to MTNS

@misc{IervTren20m,

title = {Discontinuous Lyapunov functions for discontinous piecewise-affine systems},

author = {Raffaele Iervolino and Francesco Vasca and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-ITV200122.pdf, Extended Abstract},

year  = {2020},

date = {2020-01-22},

urldate = {2020-01-22},

abstract = {Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. We first introduce the feasible Filippov solution concept by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global  asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification  of crossing, unreachable and Caratheodory boundaries. It is highlighted that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to  piecewise quadratic Lyapunov functions and using the cone-copositivity approach. },

howpublished = {Extended Abstract},

note = {accepted for cancelled MTNS 20/21},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}

@misc{Tren20m,

title = {The Laplace transform and inconsistent initial values},

author = {Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-Tre200122.pdf, Extended Abstract},

year  = {2020},

date = {2020-01-22},

urldate = {2020-01-22},

abstract = {Switches in electrical circuits may lead to Dirac impulses in the solution; a real word example utilizing this effect is the spark plug. Treating these Dirac impulses in a mathematically rigorous way is surprisingly challenging. This is in particular true for arguments made in the frequency domain in connection with the Laplace transform. A survey will be given on how inconsistent initials values have been treated in the past and how these approaches can be justified in view of the now available solution theory based on piecewise-smooth distributions.},

howpublished = {Extended Abstract},

note = {accepted for cancelled MTNS 20/21, presented at MTNS 2022},

keywords = {},

pubstate = {published},

tppubtype = {misc}

}