Stability analysis of switched linear systems with locally overlapped switching law

Combining the common Lyapunov function method and the dwell time method, we propose stability analysis tools for switched linear systems evolving on the locally overlapped switching law. These systems exist naturally in many aerospace applications, such as separation dynamical systems involving rapid and discrete variations that are specified by the predetermined separation sequence. We show that switched linear systems with locally overlapped switching law are globally asymptotically stable provided that the dwell time on some subsystems is no smaller than a fixed positive constant. This result is also extended to the case of combination of the common Lyapunov function method and the average dwell time method. We validate the proposed stability analysis tools by an example and illustrate an application to full-envelope flight controller design.