Network Essentiality

The work here involves the development of a theory providing necessary and sufficient conditions for the property of essentiality, which was first introduced and defined by Barmish and Kettani. These conditions provide means to ascertain whether the individual unknown elements of a resistive network can be characterized as having the property of essentiality, which in turn is shown to have significant impact on the manner in which their uncertain parameter values influence overall network performance. While the work is immediately motivated by circuits and power network problems, it is anticipated to be generalizable to a range of linear system fault detection problem having an underlying network structure. In particular, this concept proves useful as a technique for robust fault detection and fault isolation.