# Dwell-time control sets and applications to the stability analysis of linear switched systems

## TL;DR

This paper extends control set theory to dwell-time constrained inputs, enabling stability analysis of linear switched systems and characterization of invariant measures using a modified control set approach.

## Contribution

It introduces a new definition of control sets for dwell-time inputs, facilitating stability analysis and measure support characterization in switched systems.

## Key findings

- Characterized maximal Lyapunov exponent using periodic angular trajectories.
- Provided a framework for analyzing invariant measures in dwell-time switched systems.
- Extended control set theory to non-concatenable input classes.

## Abstract

We propose an extension of the theory of control sets to the case of inputs satisfying a dwell-time constraint. Although the class of such inputs is not closed under concatenation, we propose a suitably modified definition of control sets that allows to recover some important properties known in the concatenable case. In particular we apply the control set construction to dwell-time linear switched systems, characterizing their maximal Lyapunov exponent looking only at trajectories whose angular component is periodic. We also use such a construction to characterize supports of invariant measures for random switched systems with dwell-time constraints.