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Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in H∞ control

✍ Scribed by Lionel Rosier; Eduardo D. Sontag

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 179 KB
Volume: 41
Category: Article
ISSN: 0167-6911
DOI: 10.1016/s0167-6911(00)00060-8

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✦ Synopsis

This paper deals with the regularity of solutions of the Hamilton-Jacobi inequality which arises in H∞ control. It shows by explicit counterexamples that there are gaps between existence of continuous and locally Lipschitz (positive deÿnite and proper) solutions, and between Lipschitz and continuously di erentiable ones. On the other hand, it is shown that it is always possible to smooth-out solutions, provided that an inÿnitesimal increase in gain is allowed.