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Independent of delay stability criteria for uncertain linear state space models. (English) Zbl 0887.93048

Some elementary conditions are given for the uncertain delay system \[ \begin{aligned} \dot x(t) &= Ax(t)+ \sum^m_{i=1} \alpha_iA_ix(t)+\sum^q_{k= 1}\varepsilon_k E_kx(t-\tau_k)\\ x(t) & =\Phi(t),\quad t\leq 0\end{aligned} \] to be stable independently of the delay and the bounded uncertainties. The main result states that the system is stable if there exists \(P>0\) such that \[ PA+ A^TP+ L^TL= 0 \] for any matrix \(L\) of full rank and the uncertain parameters satisfy a suitable bound. Some examples are given.

MSC:

93D09 Robust stability
34K20 Stability theory of functional-differential equations
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