Stability criterion for a class of descriptor systems with discrete and distributed time delays. (English) Zbl 1136.34340
Conditions for global exponential stability are given for the linear descriptor delayed system
\[ \begin{cases} Ex'(t) = A_0x(t) + \sum_{i}A_i x(t-\tau_i) + \sum_j\int_{t-h_j}^t B_jx(s)\,ds, &t > 0;\\ x(t) = \phi(t), &t\leq 0,\end{cases} \]
where \(x(t)\in{\mathbb R}^n\); \(E\neq 0\), \(A_i\) and \(B_j\) are constant \(n\times n\) matrices, and \(\tau_i,h_j > 0\).
\[ \begin{cases} Ex'(t) = A_0x(t) + \sum_{i}A_i x(t-\tau_i) + \sum_j\int_{t-h_j}^t B_jx(s)\,ds, &t > 0;\\ x(t) = \phi(t), &t\leq 0,\end{cases} \]
where \(x(t)\in{\mathbb R}^n\); \(E\neq 0\), \(A_i\) and \(B_j\) are constant \(n\times n\) matrices, and \(\tau_i,h_j > 0\).
Reviewer: Mihail M. Konstantinov (Sofia)
MSC:
| 34K20 | Stability theory of functional-differential equations |
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