I am interested in understanding the behaviour of a class of continuous time switching systems of the form $\dot{x}(t) = f_{\sigma(t)}(x(t))$ where $f_{\bar{\sigma}}(x)$ is continuous for any $\bar{\sigma}$.
The particularity of this class of systems is that the switching rule $\sigma(t)$ is given by a piecewise constant function, where the intervals where it is constant have all the same length. Indeed, there is a time discretization $t_0<t_1<...<t_N=T$, where $\forall i\;\;\Delta t = t_{i+1} - t_i$ and $\sigma(t) = \lambda_i$ for $t\in [t_i,t_{i+1})$, $\lambda_i\in\{1,...,M\}$ a set of indices.
So the peculiarity is that the switching times are evenly spaced. Is this switching rule named in some way? Is there some reference where I can study it?