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Exponential stability of uncertain dynamic systems including state delay. (English) Zbl 1220.34095
Systems with uncertainties and delays, described by equations of the form $\begin{gathered} \dot x(t)= (A+\Delta A) x(t)+ (A_1+\Delta A_1) x(t- h),\\ x(s)= \phi(s),\quad s\in [-h,0]\end{gathered}$ are considered. It is assumed that the uncertain terms can be written as $$\Delta A= DF(t)E$$, $$\Delta A_1= D_1F_1(t)E_1$$, where the matrices $$D$$, $$E$$, $$D_1$$, $$E_1$$ are known, and the matrices $$F$$, $$F_1$$ are small in same sense. The main result is a sufficient condition for exponential stability, expressed in terms of a LMI where the delay $$h$$ appears explicitly. The result is illustrated by means of two examples.

##### MSC:
 34K20 Stability theory of functional-differential equations 34D10 Perturbations of ordinary differential equations 93D20 Asymptotic stability in control theory
LMI toolbox
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