Input‐To‐State Safety of Switched Systems With Single Barrier Function and Its Application to Aero‐Engine

ABSTRACT In this paper, a single barrier function (SBF) method is introduced to analyze input‐to‐state safety (ISSf) for switched systems with disturbances. Sufficient conditions are provided to ensure safety and asymptotic stability of switched systems based on the union of SBF and a single Lyapunov function. To study the safety of switched systems with disturbances, a single input‐to‐state safe barrier function is proposed, which defines the safety of switched systems with disturbances as forward invariance of a set that contains the safe set of switched systems without disturbances. Also, a tunable single input‐to‐state safe barrier function is further proposed. This function permits the size of the invariant set, which contains a safe set of switched systems without disturbances, to be tuned closer to the original safe set, offering a less conservative method for handling disturbances of switched systems. Furthermore, a novel state‐dependent switching signal with minimum dwell time is designed to avoid the Zeno phenomenon. Finally, an aero‐engine system and a numerical example are given to verify the effectiveness of the proposed method.