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On the Lyapunov approach to robust stabilization of uncertain nonlinear systems. (English) Zbl 0853.93092
Consider the uncertain dynamical system \[ \dot x = f(x,t,p) + \Delta f(x,t,p) + \bigl[ B(x,t) + \Delta B (x,t,p) \bigr] \bigl[ u(t) + d_1(x,t) \bigr] \] where \(p \in P\), a compact set, is a vector parameter, \(d_1 (x,t)\) is a known bounded disturbance, \(\Delta f\) and \(\Delta B\) are unstructured bounded uncertainties. The uncontrolled certain system \[ \dot x = f(x,t,p) \] has the zero equilibrium globally uniformly asymptotically stable with a known Lyapunov function for all \(p \in P\). The authors give conditions for the control of the form \[ u(x,t) = Y(x,t) \Psi (x,t) + \delta (x,t) \] to ensure global asymptotic stability despite the uncertainty.

MSC:
93D21 Adaptive or robust stabilization
93D30 Lyapunov and storage functions
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