The stability cone for a delay differential matrix equation

The Stability Cone for a Matrix Delay Difference Equation

Parameters of linear systems are subject to time changes. That is why in order to construct such systems it is desirable to know if they are not only stable but also able to estimate the distance of the system from the boundary of the stability region in the parameter space. Therefore, it makes sense to investigate the geometry of the subset of stable polynomials in the space of characteristic ...

Differential Equation of Sensitivity Matrix for Final Velocity Constraint

Contraction Mapping and Stability in a Delay-differential Equation

In this paper we study the stability properties of a delay differential equation by means of contraction mappings. The paper is motivated by a number of difficulties encountered in the study of stability by means of Liapunov’s direct method. We notice that most of these difficulties vanish when applying fixed point theory. An asymptotic stability theorem with a necessary and sufficient conditio...

Stability of a critical nonlinear neutral delay differential equation

This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the fact that the spectrum of the linear operator is asymptotically closed to the imaginary axis. An analysis based on the energy method provides new results about ...

Approximating the Stability Region for a Differential Equation with a Distributed Delay

Abstract. We discuss how distributed delays arise in biological models and review the literature on such models. We indicate why it is important to keep the distributions in a model as general as possible. We then demonstrate, through the analysis of a particular example, what kind of information can be gained with only minimal information about the exact distribution of delays. In particular w...