Strong Semistabilizability and Partial Semistabilizability with Applications to Semistabilization Analysis of Multi-Layer Networks

摘要

Stabilizability is a metric to measure the ability of a dynamical system to achieve asymptotic stabilization by feedback. Similar to this role, semistabilizability was originally proposed to measure the capability of a dynamical system to achieve semistable stabilization or equivalently, semistabilization by feedback. However, in this paper by conducting a further detailed discussion on the notion of semistabilizability, we find out its limitation and restriction to fully capture the semistabilization capability of linear systems. Thus, two new notions of strong semistabilizability and partial semistabilizability are proposed to fully characterize the semistabilization ability for linear systems. These notions are then used for semistabilization analysis of multi-layer networks formed by graph Cartesian products when each single layer of networks is semistabilizable.