Input-to-state stability of neutral type systems
Michael I. Gil'
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 33 (2013), p. 5-16 / Harvested from The Polish Digital Mathematics Library
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We consider the system ẋ(t)-∫₀ηdR̃(τ)ẋ(t-τ)=∫0ηdR(τ)x(t-τ)+[Fx](t)+u(t) (ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered systems, and the Ostrowski inequality for determinants.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:270674 
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     year = {2013},
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Michael I. Gil'. Input-to-state stability of neutral type systems. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 33 (2013) pp. 5-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1143/

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