Semi-global finite-time observers for nonlinear systems

By Yanjun Shen, Xiaohua Xia. at - Automatisierungstechnik, 2008

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Continuous output‐feedback finite‐time control for a class of second‐order nonlinear systems with disturbances (2016, background): “After that, Shen and Xia proposed a finite-time convergent observer for a single output nonlinear system [34], but the observer is only semi-global.”
Technical Notes and Correspondence Uniformly Observable and Globally Lipschitzian Nonlinear Systems Admit Global Finite-Time Observers (2009, methodology): “the system (18) can be rewritten as . Then . Using the same method in [ 21 ], we can obtain that in (20) satisfies”
Prescribed-Time Control and Its Latest Developments (2022, background): “Proposition 2 [69]: For system ẋ = f (x, t), if there exists a C1 function V(x) ≥ 0 such that V̇(x) ≤ −k1Vq(x)+ k2V(x) where k1 > 0, k2 > 0, and 0 < q < 1, then the closedloop system is semi-global FT stable and the settling time is calculated by”
Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time (2017, background): “E-mail addresses: ydsong@cqu.edu.cn (Y. Song), iamwyj123456789@163.com (Y. Wang), jchollow@ucsd.edu (J. Holloway), krstic@ucsd.edu (M. Krstic). the ‘‘Lyapunov differential inequality’’ introduced by Bhat and Bernstein (2000) and refined by Shen and Xia (2008) and Shen and Huang (2012).”