On the Stability of Switched ARX Models, with an Application to Learning via Regression Trees

This work studies the stability properties of Switched AutoRegressive eXogenous (SARX) models subject to arbitrary switching sequences. We provide necessary and sufficient conditions for the arbitrary switching stability of multiple-input single-output SARX models under nonnegativity constraints, and sufficient-only conditions removing sign constraints. The conditions are equivalently formulated on state-space representations of SARX models, due to their influential use in designing control strategies. As an application of the aforementioned results, we propose a novel algorithm for the identification of switched models with stability guarantees via Regression Trees, a powerful machine learning technique.