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On the control of uncertain impulsive systems: approximate stabilization and controlled invariance. (English) Zbl 1070.93041
Authors’ abstract: The problems of stabilization and controlled invariance of a fairly wide class of uncertain hybrid systems is considered. Uncertainty enters in the form of a disturbance input that can affect both the continuous and the discrete dynamics. A method for designing piecewise constant feedback controllers for this class of systems is developed. In the case of controlled invariance, the controller ensures that the state of the system remains arbitrarily close to a desired set over an arbitrarily long time horizon. In the case of stabilization, the controller ensures approximate exponential convergence of the runs of the closed-loop system to the zero-level set of a Lyapunov function.

MSC:
93D21 Adaptive or robust stabilization
34A37 Ordinary differential equations with impulses
93C73 Perturbations in control/observation systems
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