Taming Heterogeneity and Complexity of Embedded Control

Further Remarks on Stability Crossing Curves of Distributed Delay Systems

 

Constantin Irinel Morărescu¹-Silviu-Iulian Niculescu²

¹HeuDiaSyC (UMR CNRS 6599) Université de Technologie de Compiègne Centre de Recherche de Royallieu BP 20529, 60205, Compiègne, France. The author is also with the Department of Mathematics, University “Politehnica” of Bucharest, Romania

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²HeuDiaSyC (UMR CNRS 6599) Université de Technologie de Compiègne Centre de Recherche de Royallieu BP 20529, 60205, Compiègne, France. [e-mail]

ABSTRACT. This paper focuses on the problem of robust stability with delay deviation for a linear system including a gamma-distributed delay with a gap. First, we present the stability analysis of such dynamical systems in the space defined by the (mean-delay,gap)-parameters. Next, we present an analytical method to compute the maximum radius of delay deviation without changing the number of unstable roots of the corresponding characteristic equation. The stability crossing curves, derived in some of our previous works, will play a major role in deriving such robustness measure. Illustrative examples complete the presentation.

KEYWORDS: Stability; distributed delay; gamma-distribution; crossing curves

1. Introduction and motivating examples

It is well known that the delays appear naturally in many dynamical systems in physics, population dynamics and biology, economy and engineering for describing transport and propagation phenomena and/or heredity ...