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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.

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