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There is a direct criterion for the stability of regular descriptor linear systems which indicates that the stability of the system (1) is totally determined by spectrum of the matrix pencil σ ( E, A ) [6].
(ii) Matrix pencil ( E, A ) with no finite eigenvalue .
Matrix pencil ( E, A ) with no finite eigenvalues.
Matrix pencil ( E, A ) with at least one finite eigenvalue.
These conditions are placed on the matrix pencil Aλ−B.
Figure 6 Sparsity of matrix pencil ( E, A ). Figure 7 Sparsity of matrix pencil ( E ˜, A ˜ ). Figure 8 Output solutions of Example 5.
A matrix pencil is a family of matrices sF - G, parametrized by a complex number s.
(i) Matrix pencil ( E, A ) with at least one finite eigenvalue .
Moreover, this decoupling preserves the spectrum of the matrix pencil ( E, A ) of the DAE.
From decoupled system (5a - 5c) we obtain: (14) (ii) Matrix pencil ( E, A ) with no finite eigenvalues .
The sparsity of the matrix pencil of this DAE system is shown in Figure 6.
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