# Input-to-state stability of neutral type systems

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

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

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topMichael 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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