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Stabilizability and controllability of systems associated to linear skew-product semiflows.

Mihail Megan, Adina Luminita Sasu, Bogdan Sasu (2002)

Revista Matemática Complutense

This paper is concerned with systems with control whose state evolution is described by linear skew-product semiflows. The connection between uniform exponential stability of a linear skew-product semiflow and the stabilizability of the associated system is presented. The relationship between the concepts of exact controllability and complete stabilizability of general control systems is studied. Some results due to Clark, Latushkin, Montgomery-Smith, Randolph, Megan, Zabczyk and Przyluski are generalized....

Steady state in a biological system: global asymptotic stability

Maria Adelaide Sneider (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A suitable Liapunov function is constructed for proving that the unique critical point of a non-linear system of ordinary differential equations, considered in a well determined polyhedron K , is globally asymptotically stable in K . The analytic problem arises from an investigation concerning a steady state in a particular macromolecular system: the visual system represented by the pigment rhodopsin in the presence of light.

Substitution method for generalized linear differential equations

Dana Fraňková (1991)

Mathematica Bohemica

The generalized linear differential equation d x = d [ a ( t ) ] x + d f where A , f B V n l o c ( J ) and the matrices I - Δ - A ( t ) , I + Δ + A ( t ) are regular, can be transformed d y d s = B ( s ) y + g ( s ) using the notion of a logarithimc prolongation along an increasing function. This method enables to derive various results about generalized LDE from the well-known properties of ordinary LDE. As an example, the variational stability of the generalized LDE is investigated.

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