Input-to-state stability of neutral type systems

Michael I. Gil'

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)

  • Volume: 33, Issue: 1, page 5-16
  • ISSN: 1509-9407

Abstract

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We consider the system ẋ ( t ) - ∫ ₀ η d R ̃ ( τ ) ẋ ( t - τ ) = ∫ 0 η d R ( τ ) x ( t - τ ) + [ F x ] ( 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.

How to cite

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Michael I. Gil'. "Input-to-state stability of neutral type systems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 33.1 (2013): 5-16. <http://eudml.org/doc/270674>.

@article{MichaelI2013,
abstract = {We consider the system $ẋ(t) - ∫₀^\{η\} dR̃(τ) ẋ(t-τ) = ∫_0^\{η\} dR(τ)x(t-τ) + [Fx](t) + u(t)$ (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.},
author = {Michael I. Gil'},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {neutral type systems; causal mappings; input-to-state stability},
language = {eng},
number = {1},
pages = {5-16},
title = {Input-to-state stability of neutral type systems},
url = {http://eudml.org/doc/270674},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Michael I. Gil'
TI - Input-to-state stability of neutral type systems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2013
VL - 33
IS - 1
SP - 5
EP - 16
AB - We consider the system $ẋ(t) - ∫₀^{η} dR̃(τ) ẋ(t-τ) = ∫_0^{η} dR(τ)x(t-τ) + [Fx](t) + u(t)$ (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.
LA - eng
KW - neutral type systems; causal mappings; input-to-state stability
UR - http://eudml.org/doc/270674
ER -

References

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