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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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