Mathematics

In this talk we discuss the connection between commutation relations among a family of asymptotically stable vector fields and stability properties of the corresponding switched system (or, more generally, a differential inclusion). We review some known results for the linear case and then present new results for the nonlinear case. The proof of the main new result involves considering an optimal control problem of finding the "most unstable" trajectory for an associated control system, and showing that there exists an optimal solution which is bang-bang with a bound on the total number of switches.