Constructive stabilization of quadratic-input nonlinear systems with bounded controls. (English) Zbl 1203.93185
Summary: The stabilization of quadratic-input nonlinear systems with bounded controls is considered. According to the type of quadratic-input forms, two cases, namely, positive definite and positive semi-definite, are considered. For the case of positive definiteness, a universal formula for bounded stabilizers is given via a known Lyapunov control function. For the case of positive semidefiniteness, a constructive parametrization of bounded stabilizers is proposed under the assumption that there exists a known Lyapunov control function with respect to a smaller control set than the admissible control set.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93D30 | Lyapunov and storage functions |
| 93C10 | Nonlinear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
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