D ec 1 99 9 Remarks regarding the gap between continuous , Lipschitz , and differentiable storage functions for dissipation inequalities appearing in H ∞ control Lionel Rosier
نویسنده
چکیده
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 definite and proper) solutions, and between Lipschitz and continuously differentiable ones. On the other hand, it is shown that it is always possible to smooth-out solutions, provided that an infinitesimal increase in gain is allowed.
منابع مشابه
Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in H∞ control
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 definite and proper) solutions, and between Lipschitz and continuously differentiable ones. On the other hand, it is shown that it is always possible to smooth-out ...
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