A Graph Approach to Observability in Physical Sparse Linear Systems

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="305415.fig.003a" src="https://static.hindawi.com/articles/jam/volume-2012/305415/figures/305415.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>associated network <svg height="12.3" id="M427" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.7125 12.3" width="14.7125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,11.675)"><use xlink:href="#x1D44B"></use></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="305415.fig.003b" src="https://static.hindawi.com/articles/jam/volume-2012/305415/figures/305415.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>spanning tree <svg height="12.7375" id="M428" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.5625 12.7375" width="12.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,12.112)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g>
</svg></td></tr></table></td></tr></table>

<table>Four-node network example.</table>

Journal of Applied Mathematics

fig3

Figure 3

Figure 3: A Graph Approach to Observability in Physical Sparse Linear Systems 