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

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

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

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

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

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

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