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Journal Articles Mathematical Control and Related Fields Year : 2015

Zubov's equation for state-constrained perturbed nonlinear systems

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Abstract

The paper gives a characterization of the uniform robust domain of attraction for a nite non-linear controlled system subject to perturbations and state constraints. We extend the Zubov approach to characterize this domain by means of the value function of a suitable in nite horizon state-constrained control problem which at the same time is a Lyapunov function for the system. We provide associated Hamilton-Jacobi-Bellman equations and prove existence and uniqueness of the solutions of these generalized Zubov equations.
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Dates and versions

hal-00931028 , version 1 (14-01-2014)

Identifiers

Cite

Lars Grüne, Hasnaa Zidani. Zubov's equation for state-constrained perturbed nonlinear systems. Mathematical Control and Related Fields, 2015, 5 (1), pp.55-71. ⟨10.3934/mcrf.2015.5.55⟩. ⟨hal-00931028⟩
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