9,001 research outputs found
Positive Realness of a Transfer Function Neither Implies Nor is Implied by the External Positivity of their Associate Realizations
This letter discusses the differences between the properties of positive
realness of transfer functions and external positivity in linear time-invariant
dynamic systems. It is proved that each one of both properties does not imply
to each other.Comment: 5 page
A Generalization of Halpern Iteration. Preliminary Results
A generalization of a viscosity generalized Halpern iteration scheme is
analyzed. It is proven that the solution converges asymptotically strongly to a
unique fixed point of an asymptotically nonexpansive mapping which drives the
iteration together with a contractive self-mapping, a viscosity term and two
driving external forcing terms
Asymptotic Behavior of Systems involving Delays: Preliminary Results
This paper investigates the relations between the particular eigensolutions
of a limiting functional differential equation of any order, which is the
nominal (unperturbed) linear autonomous differential equations, and the
associate ones of the corresponding perturbed functional differential equation.
Both differential equations involve point and distributed delayed dynamics. The
proofs are based on a Perron type theorem for functional equations so that the
comparison is governed by the real part of a dominant zero of the
characteristic equation of the nominal differential equation. The obtained
results are also applied to investigate the global stability of the perturbed
equation based on that of its corresponding limiting equation.Comment: 32 page
Mixed Non-Expansive and Potentially Expansive Properties of a Class of Self-Maps in Metric Spaces
This paper investigates self-maps T from X to X which satisfy a distance
constraint in a metric space which mixed point-dependent non-expansive
properties, or in particular contractive ones, and potentially expansive
properties related to some distance threshold. The above mentioned constraint
is feasible in certain real -world problems.Comment: 9 page
On best proximity points of multivalued cyclic self-mappings endowed with a partial order
The existence and uniqueness of fixed points of both the cyclic self-mapping
and its associate composite self-mappings on each of the subsets are
investigated if the subsets in the cyclic disposal are nonempty, bounded and of
nonempty convex intersection is investigate
About Adaptive Singular Systems with External Delay
This paper is mainly concerned with the robustly stable adaptive control of
single-input single-output impulse-free linear time-invariant singular dynamic
systems of known order and unknown parameterizations subject to single external
point delays. The control law is of pole-placement type and based on
input/output measurements and parametrical estimation only. The parametrical
estimation incorporates adaptation dead zones to prevent against potential
instability caused by disturbances and unmodeled dynamics. The Weierstrass
canonical form is investigated in detail to discuss controllability and
observability via testable conditions of the given arbitrary state-space
realization of the same order.Comment: 28 page
Analysis of Caputo linear fractional dynamic systems with time delays through fixed point theory
This paper investigates the global stability and the global asymptotic
stability independent of the sizes of the delays of linear time-varying Caputo
fractional dynamic systems of real fractional order possessing internal point
delays. The investigation is performed via fixed point theory in a complete
metric space by defining appropriate non-expansive or contractive self-
mappings from initial conditions to points of the state- trajectory solution.
The existence of a unique fixed point leading to a globally asymptotically
stable equilibrium point is investigated in particular under easily testable
sufficiency-type stability conditions. The study is performed for both the
uncontrolled case and the controlled case under a wide class of state feedback
laws
Preliminaries on best proximity points in cyclic multivalued mappings
This paper investigates the fixed points and best proximity points of
multivalued cyclic self-mappings in metric spaces under a generalized
contractive condition involving Hausdorff distances
On Chebyshev systems and non-uniform sampling related to controllability and observability of caputo fractional differential systems
This paper is concerned with the investigation of the controllability and
observability of Caputo fractional differential linear systems of any real
order {\alpha} . Expressions for the expansions of the evolution operators in
powers of the matrix of dynamics are first obtained. Sets of linearly
independent continuous functions or matrix functions, which are also Chebyshev
systems, appear in such expansions in a natural way. Based on the properties of
such functions, the controllability and observability of the Caputo fractional
differential system of real order {\alpha} are discussed as related to their
counterpart properties in the corresponding standard system defined for
{\alpha} = 1. Extensions are given to the fulfilment of those properties under
non- uniform sampling. It is proved that the choice of the appropriate sampling
instants ion not restrictive as a result of the properties of the associate
Chebyshev system
Preliminaries on pseudo-contractions in the intermediate sense for non-cyclic and cyclic self-mappings in metric spaces
A contractive condition is addressed for extended 2-cyclic self-mappings on
the union of a finite number of subsets of a metric space which are allowed to
have a finite number of successive images in the same subsets of its domain. It
is proven that if the space is uniformly convex and the subsets are non-empty,
closed and convex then all the iterations converge to a unique closed limiting
finite sequence which contains the best proximity points of adjacent subsets
and reduce to a unique fixed point if all such subsets intersect.Comment: arXiv admin note: text overlap with arXiv:1208.075
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