This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets Γ1 C Γ2 C Rn, with Γ1 compact, the theorems presented in this paper give conditions under which a qualitative property of Γ1 that holds relative to Γ2 (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set Γ1, then Γ1 is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal.

Reduction Theorems for Hybrid Dynamical Systems / Maggiore, M.; Sassano, M.; Zaccarian, L.. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - 64:6(2019), pp. 2254-2265. [10.1109/TAC.2018.2861364]

Reduction Theorems for Hybrid Dynamical Systems

Zaccarian L.
2019

Abstract

This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets Γ1 C Γ2 C Rn, with Γ1 compact, the theorems presented in this paper give conditions under which a qualitative property of Γ1 that holds relative to Γ2 (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set Γ1, then Γ1 is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal.
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Maggiore, M.; Sassano, M.; Zaccarian, L.
Reduction Theorems for Hybrid Dynamical Systems / Maggiore, M.; Sassano, M.; Zaccarian, L.. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - 64:6(2019), pp. 2254-2265. [10.1109/TAC.2018.2861364]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/259055
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