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Zbl 1044.34031
Liu, Xinzhi; Shen, Xuemin; Zhang, Yi
Exponential stability of singularly perturbed systems with time delay. (English)
[J] Appl. Anal. 82, No. 2, 117-130 (2003). ISSN 0003-6811; ISSN 1563-504X/e

For the linear system $$\alignat2 & \dot{x}(t)=A_{11}(t)x(t)+A_{12}(t)x(t-\tau)+B_{12}(t)z(t) + B_{12}(t)z(t-\tau),&\quad&x(t)\in \Bbb R^n,\\ & \varepsilon\dot{z}(t)=A_{21}(t)+A_{22}(t)+x(t-\tau)+B_{21}(t)z(t),&\quad&z(t)\in \Bbb R^m, \endalignat$$ and for the nonlinear system $$\align & \dot{x}(t)=A_{11}x(t)+g(x(t),x(t-\tau),z(t),z(t-\tau)),\\ &\varepsilon \dot{z}(t)=B_{21}z(t)+B(x(t),x(t-\tau)), \endalign $$ criteria for the exponential stability are derived.
[Tamaz Tadumadze (Tbilisi)]

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K26 Singular perturbations of functional-differential equations

Keywords: singular perturbation; time delay; exponential stability

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