Strong Structural Controllability and Zero Forcing

In this chapter, we study controllability and output controllability of systems defined over graphs. Specifically, we consider a family of state-space systems, where the state matrix of each system has a zero/non-zero structure that is determined by a given directed graph. Within this setup, we investigate under which conditions all systems in this family are controllable, a property referred to as strong structural controllability. Moreover, we are interested in conditions for strong structural output controllability. We will show that the graph-theoretic concept of zero forcing is instrumental in these problems. In particular, as our first contribution, we prove necessary and sufficient conditions for strong structural controllability in terms of so-called zero forcing sets. Second, we show that zero forcing sets can also be used to state both a necessary and a sufficient condition for strong structural output controllability. In addition to these main results, we include interesting results on the controllability of subfamilies of systems and on the problem of leader selection.</p

わが国における最低資本金規制の導入と廃止

I.はじめに II. 株式会社と資本確定 III. わが国における最低資本金制度の変遷 IV. 欧米の最低資本金制度 V. 導入，強化の目的とその背景 VI.緩和，廃止の目的とその背景 VII.小

When a workforce strategy won't work : critique on current policy direction in England, UK

“The final, definitive version of this article has been published in the Journal, Journal of Intellectual Disabilities: JOID, Vol.14 Issue 4, 2010, Copyright SAGE Publications Ltd on SAGE Journals Online: http://online.sagepub.com/ "This editorial is based on findings from a regional review of educational commissioning, and workforce issues for one Strategic Health Authority in England. Known as the ‘Valued People Project’ (VPP) it commenced in May 2008 and was undertaken in response to expressed concerns by regional key stakeholders regarding education commissioning specifically of pre-registration learning disability nursing, and the contribution of the specialist learning disability health workforce more generally (Gates, 2009). This work was also undertaken as a consequence of the scale and cumulative effect of changes to education, workforce, professional regulation and central health and social care policy that has affected people with learning disabilities, and the services and personnel that support them.Peer reviewedFinal Accepted Versio