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A remark on Lagrange stability of nonlinear systems stabilization. (English) Zbl 0773.93058

The problem of stability (in the sense of Lagrange) for nonlinear control systems is considered. For simplificity only the single input-single output systems are treated. It is proved under suitable assumptions, that if there is a bounded input \(u\) such that the corresponding output is bounded for any initial condition, then the system is \(u\)-Lagrange stable. Furthermore, some assumptions are proposed under which the Lagrange stability with respect to any bounded input implies existence of a stability feedback law.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C10 Nonlinear systems in control theory
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References:

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