Course name: Advanced topics in control
Prof. Florian Dorfler
March 3, 2016
Course website: http://control.ee.ethz.ch/~ifaatic/
Lecture 1: Elements of matrix theory
In motivating examples such as distributed estimation in sensor networks and social opinion dynamics, problems can be formally posed in the following iteration operations:
[math]x^{+}=Ax[/math],
with the following properties:
-sparsity pattern induced by graph
-nonnegative coefficents: [math]a_{ij}\geq 0[/math]
-unit row sums: [math]\sum_{j}a_{ij}=1[/math]
Here comes the question: is such an iteration convergent and what is it converging to. This topic will be discussed in the following two lectures using different approach(matrix theory approach and graph theory approach)