Abstract
In this paper, it is shown that the minimal time function is locally Lipschitz continuous for the control systemx′=Ax+u in a Banach spadeE, under either of two conditions:A is linear and generates aC 0-semigroup of bounded linear operators; orA is nonlinear, possibly multivalued, and dissipative. The main tool used for the nonlinear case is a result of Barbu concerning the null controllability of the system.
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Communicated by R. Conti
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Cârja, O. On the minimal time function for distributed control systems in Banach spaces. J Optim Theory Appl 44, 397–406 (1984). https://doi.org/10.1007/BF00935459
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DOI: https://doi.org/10.1007/BF00935459