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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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