Tuesday 16 Mar 2021: Noisy boundaries and stochastics saltation matrices
Petri Piiroinen - Chalmers University of Technology
https://Universityofexeter.zoom.us/j/92988302721?pwd=U1h1ZGtkdXFydmVBY1U5T0FpdDlNdz09 Meeting ID: 929 8830 2721 Password: 468554 13:30-14:30
In a smooth dynamical system the local stability of a given reference trajectory can be determined by examining the linearized system about the trajectory. For a piecewise-smooth system one can introduce the additional concept of a saltation matrix that allows for linearization when the system undergoes a discrete jump or has a discontinuous vector field. Here we will further broaden the scope for what trajectories can be analysed by introducing the stochastic saltation matrix, which allows for the linearization of discontinuous systems with stochastically oscillating boundaries or boundaries with stochastic surface profiles. We will see how such matrices can be used to estimate the dynamic effects of systems with noisy boundaries through a few examples, including the famous Chua circuit.