In this paper we extend well-known relationships between global asymptotic controllability, sample stabilizability, and the existence of a control Lyapunov function to a wide class of control systems with unbounded controls, including control-polynomial systems. In particular, we consider open loop controls and discontinuous stabilizing feedbacks, which may be unbounded approaching the target, so that the cor- responding trajectories may present a chattering behaviour. A key point of our results is to prove that global asymptotic controllability, sample stabilizability, and existence of a control Lyapunov function for these systems or for an impulsive extension of them are equivalent.
Converse Lyapunov theorems for control systems with unbounded controls
Motta, Monica
2022
Abstract
In this paper we extend well-known relationships between global asymptotic controllability, sample stabilizability, and the existence of a control Lyapunov function to a wide class of control systems with unbounded controls, including control-polynomial systems. In particular, we consider open loop controls and discontinuous stabilizing feedbacks, which may be unbounded approaching the target, so that the cor- responding trajectories may present a chattering behaviour. A key point of our results is to prove that global asymptotic controllability, sample stabilizability, and existence of a control Lyapunov function for these systems or for an impulsive extension of them are equivalent.File | Dimensione | Formato | |
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ConverseLT_LM_review_1.pdf
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