Lie-Algebraic Stability Criteria for Switched Systems

By Andrei A. Agrachev, Daniel Liberzon. SIAM Journal of Control and Optimization, 2001

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On common quadratic Lyapunov functions for stable discrete‐time LTI systems (2004, methodology): “…a considerable body of literature dedicated to this question for both discrete-time and continuous-time systems (Boyd and Yang 1989), (Ando 2001), (Agrachev and Liberzon 2001), (Shorten and Narendra 1999), (Akar and Narendra 2001), (Gurvits 1995), (Ooba and Funahashi 1999), (Ooba and Funahashi…”
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results (2009, background): “linear systems [1], [48] to obtain local stability results based on”
Stability Criteria for Switched and Hybrid Systems (2007, neutral): “The most general result along these lines is the following theorem due to Agrachev and Liberzon [2].”
Review on computational methods for Lyapunov functions (2015, background): “, given in Agrachev and Liberzon 2001 [2], where even though every convex combination”
Stability and persistent disturbance attenuation properties for a class of networked control systems: switched system approach (2005, positive): “In Liberzon et al. (1999) and Agrachev and Liberzon (2001), Lie algebra conditions were given which imply the existence of a common quadratic Lyapunov function.”