I just noticed that the textbook lacks an example relevant to this exercise group, which is a type of problem we frequently assess: Given a piecewise-defined function, we want to know if it is ...

Abstract: We propose a novel characterization of piecewise-defined barrier functions for certifying forward invariant sets of piecewise continuous dynamical systems. Forward invariance is established ...

Abstract: Oscillations appear in numerous applications from biology to technology. However, besides local results, rigorous stability and robustness analysis of oscillations are rarely done due to ...