## Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty.(English)Zbl 1008.93056

The following system with uncertainty is considered $\dot{x}(t)=[A+\Delta A(t)]x(t)+[A_{1}+\Delta A_{1}(t)]x(t-\tau(t)),$ where $\Delta A(t)=DF_{0}(t)E,\quad \Delta A_{1}(t)=D_{1}F_{1}(t)F_{1},\quad \|F_{i}(t)\|\leq 1,\;i=0,1;$
$0\leq\tau(t)\leq h,\qquad \dot{\tau}(t)\leq d<1.$
A sufficient condition of robust stability of the zero solution is obtained in the form of an LMI, which contains both the size and the time derivative of the time delay.

### MSC:

 93D09 Robust stability 93C23 Control/observation systems governed by functional-differential equations
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