Necessary and sufficient stability condition for second-order switched systems: a phase function approach

摘要

To find a unified approach for the stability analysis of second-order switched system, the concept of phase function is proposed in this paper. First, the basic properties of phase function are explored. Following this concept and its properties, the phase-based stability criterion is investigated based on the Lyapunov theory, and a necessary and sufficient stability condition is obtained in the phase function approach. Moreover, the connection between phase-based stability conditions and algebraic condition of system matrices is also discussed. Finally, numerical examples are provided to exemplify the main result and make necessary comparisons with the existing methods.