Recent Results on the Stability and Response Bounds of Linear Systems: A Review

TLDR: The literature on linear systems emerging from second order differential equations is extensive because such systems are ubiquitous in modeling, particularly modeling of mechanical systems as mentioned in this paper. But this paper is not a comprehensive overview of the recent research in this field.

Abstract: The literature on linear systems emerging from second order differential equations is extensive because such systems are ubiquitous in modeling, particularly modeling of mechanical systems. This paper offers an overview of some of the recent research in this field, in particular on the subject of stability and response bounds of linear systems. In addition to reporting some interesting recent stability investigations, the basic concepts of stability are reviewed, and a short introduction to Lyapunov's direct method is also presented. Particularly important for applications are response bounds for stable linear systems; therefore a comprehensive section has been devoted to this specific subject.