Finite-Time Observers: Application to Secure Communication

By Wilfrid Perruquetti, Thierry Floquet, Emmanuel Moulay. IEEE Transactions on Automatic Control, 2008

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Semi-global finite-time observers for nonlinear systems (2008, background): “The above construction of homogeneity and proof are also similar to those in Perruquetti et al. (2008), which are actually rooted in Bhat and Bernstein (2000).”
On the convergence of an extended state observer for nonlinear systems with uncertainty (2011, background): “14) is Hurwitz, it follows from [27] that for some α ∈  2 3 , 1  , the system ẏ(t) = F(y(t)) is finitetime stable.”
Sliding mode control design using canonical homogeneous norm (2019, background): “f ( z ||z|| ) (14) is asymptotically stable, where ||z|| =√z⊤Pz with P satisfying (5).”
Lyapunov Approach for Analysis and Design of Second Order Sliding Mode Algorithms (2011, methodology): “This is a distinguishing feature of our method compared to the ones in the literature for continuous and homogeneous algorithms [1, 36].”
Finite-time and fixed-time stabilization: Implicit Lyapunov function approach (2015, background): “…may also appear in observation problems when a finitetime convergence of the state estimate to the real values is required: Bejarano and Fridman (2010), Engel and Kreisselmeier (2002), Menard, Moulay, and Perruquetti (2010), Perruquetti, Floquet, and Moulay (2008), Shen, Huang, and Gu (2011).”