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Werner Krabs 《Journal of Difference Equations and Applications》2013,19(12):1107-1118
In this paper stability and attractivity in non-autonomous time-discrete dynamical systems is investigated with the aid of Lyapunov functions. The results are applied to the problem of stabilization of controlled systems by feedback controls. In the final section of the paper we give sufficient conditions for norm-bounded null-controllability of linear systems. 相似文献
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Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time
Luc Miller 《Journal of Differential Equations》2004,204(1):202-226
Given a control region Ω on a compact Riemannian manifold M, we consider the heat equation with a source term g localized in Ω. It is known that any initial data in L2(M) can be steered to 0 in an arbitrarily small time T by applying a suitable control g in L2([0,T]×Ω), and, as T tends to 0, the norm of g grows like exp(C/T) times the norm of the data. We investigate how C depends on the geometry of Ω. We prove C?d2/4 where d is the largest distance of a point in M from Ω. When M is a segment of length L controlled at one end, we prove for some . Moreover, this bound implies where is the length of the longest generalized geodesic in M which does not intersect Ω. The control transmutation method used in proving this last result is of a broader interest. 相似文献
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