论文信息 - Strong stability of elastic control systems with dissipative saturating feedback

Strong stability of elastic control systems with dissipative saturating feedback

Abstract We will consider, with a focus on saturating feedback control laws, two problems associated with damping in a bounded acoustic cavity Ω⊂ R 3 . Our objective is to verify (compare (Discrete Continuous Dynamical Systems 7 (2001) 319, Math. Control Signals Systems 2 (1989) 265) that these are strongly stable: for every finite-energy solution, the acoustic energy goes to zero as t→∞. We will, in each case, formulate the problem in terms of a contraction semigroup of nonlinear operators on an appropriate Hilbert space and compare this with the corresponding semigroups without saturation—following Avalos and Lasiecka (Semigroup Forum 57 (1998) 278) in using the spectral methods of Arendt and Batty (Trans. Amer. Math. Soc. 8 (1988) 837) to show strong stabilization for those linear semigroups.

Irena Lasiecka | Thomas I. Seidman

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