Stability of piecewise linear systems revisited

Piecewise linear systems are important in representing and approximating many practical systems with complex dynamics. While stability analysis of switched linear systems are notoriously challenging, several powerful tools have been developed to cope with the challenges. This paper provides a brief survey on stability of piecewise linear systems. The approaches introduced here range from the Lyapunov method to switching-transition-based analysis, and the combined. Main features and advantages of each approach are discussed and compared. Numerical examples and a case study are also presented to illustrate the effectiveness of the approaches.