In this paper, the authors give a necessary and sufficient condition for globally stabilizing a nonlinear system, robustly with respect to unstructured uncertainties ( ~ u; x; t); norm-bounded for each fixed x and u: This condition requires one to find a smooth, proper, and positive definite solution V (x) of a suitable partial differential inequality depending only on the system data. A procedure, based on the knowledge of V (x); is outlined for constructing almost smooth robustly stabilizing controllers. Our approach, based on Lyapunov functions, generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization, on one hand, and H1-control sector conditions and input-to-state stabilization on the other.
Robust stabilization of nonlinear systems with pointwise norm bounded uncertainties: a control Lyapunov function approach / Battilotti, Stefano. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - STAMPA. - 44:1(1999), pp. 3-17. [10.1109/9.739061]
Robust stabilization of nonlinear systems with pointwise norm bounded uncertainties: a control Lyapunov function approach
BATTILOTTI, Stefano
1999
Abstract
In this paper, the authors give a necessary and sufficient condition for globally stabilizing a nonlinear system, robustly with respect to unstructured uncertainties ( ~ u; x; t); norm-bounded for each fixed x and u: This condition requires one to find a smooth, proper, and positive definite solution V (x) of a suitable partial differential inequality depending only on the system data. A procedure, based on the knowledge of V (x); is outlined for constructing almost smooth robustly stabilizing controllers. Our approach, based on Lyapunov functions, generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization, on one hand, and H1-control sector conditions and input-to-state stabilization on the other.File | Dimensione | Formato | |
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