Stability and Stabilization of Coupled Jump Diffusions and Applications

TL;DR

This paper establishes stability and stabilization criteria for complex coupled jump diffusion systems, with applications to linearizable, fast-slow, and leader-following systems, enhancing understanding of their stability behavior.

Contribution

It provides new sufficient conditions for stability and stabilization of fully coupled jump diffusions, including various specific system types and applications.

Findings

Derived stability conditions for coupled jump diffusions

Analyzed stabilization of linearizable and fast-slow systems

Examined consensus in leader-following systems

Abstract

This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (component) is operated under the influence of other subsystems (components). This paper derives sufficient conditions under which the underlying coupled jump diffusion is stable. The results are then applied to investigate the stability of linearizable jump diffusions, fast-slow coupled jump diffusions. Moreover, weak stabilization of interacting systems and consensus of leader-following systems are examined.