A new delay-dependent criterion for neutral systems with multiple delays
This paper is concerned with the asymptotic stability of neutral delay differential systems of the form NEWLINE\[NEWLINEx'(t)= A x(t) + \sum_{i=1}^m B_i x(t- h_i) + \sum_{i=1}^m C_i x'(t - h_i),NEWLINE\]NEWLINE where \( x(t)\) is the state vector, \( A, B_i, C_i \) are constant matrices and \( h_i\) are constant bounded delays. Further, \(A\) is assumed to be a Hurwitz matrix.NEWLINENEWLINENEWLINEIn this context, the author proves a theorem which provides a delay-dependent sufficient condition for the asymptotic stability. Since this sufficient condition depends on the existence of suitable constant matrices \( P, Q_i, X_i, Y_i, Z_i \) such that a big matrix \( \Sigma = \Sigma ( P, Q_i, X_i, Y_i, Z_i)\) depending on these matrices is negative definite, the proposed sufficient condition seems to be appropriate for checking the stability of low dimensional problems as shown for a two-dimensional system with two delays. Finally, as remarked by the author, the sufficient stability condition may be weaker than other similar sufficient conditions based on the logarithmic norm of \(A\).
scientific article; zbMATH DE number 1669985