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Universal stabilization of feedforward nonlinear systems. (English) Zbl 1010.93080

The author considers the following class of locally Lipschitz feedforward nonlinear systems \[ \begin{aligned} &\dot x_1 = x_2+\varphi_1(x_3,\dots,x_n,u),\\ &\dot x_2 = x_3+\varphi_2(x_4,\dots,x_n,u),\\ &\vdots\\ &\dot x_{n-1} = x_n+\varphi_{n-1}(u),\\ &\dot x_n = u, \end{aligned}\tag{1} \] where \(x=[x_1,\dots,x_n]^T\in\mathbb{R}^n\) is the state, \(u\in\mathbb{R}\) is the control and \(\varphi_i\) are unknown functions vanishing at zero. The distinguished feature of this paper is that the design of a global stabilizer does not require a priori information on the functions \(\varphi_i\).

MSC:

93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
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