Stability and Boundary Stabilization of 1-D Hyperbolic Systems by Georges Bastin & Jean-Michel Coron

Author:Georges Bastin & Jean-Michel Coron
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Remark 4.16.

It is worth noting that Assumption 4.14 is generic. Indeed it is satisfied as soon as the eigenvalues of the matrix F(0) are distinct. But, there are interesting cases where there is a matrix Q satisfying equality (4.101) even with non-distinct eigenvalues. For example, in the case where the matrix A(Z) is block diagonal, it may be sufficient to have distinct eigenvalues in each block, but the different blocks may share identical eigenvalues. This situation will appear in particular in the proofs of Theorems 4.22 and 4.24 which deal with stability for C p -norms with p > 1 and for H p -norms with p > 2.

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