# Course

## ME269,ECE269 - Network Systems

Units: 4

*Instructor(s): * Bullo

*Syllabus: *

Motivating socio/economic networks, power grids, multi-agent robotics. Perron-Frobenius matrix theory and algebraic graph theory. Fundamental dynamics in networks: averaging dynamics in discrete and continuous time; positive and compartmental systems; coupled oscillator systems; virus propagation models; population dynamic models; robotic coordination problems.

*Detailed description: *

Motivating socio/economic networks, power grids, multi-agent robotics. Perron-Frobenius matrix theory and algebraic graph theory. Fundamental dynamics in networks: averaging dynamics in discrete and continuous time; positive and compartmental systems; coupled oscillator systems; virus propagation models; population dynamic models; robotic coordination problems.

The course is intended primarily for graduate students interested in network science, dynamics over networks, cooperative and distributed control, distributed systems, and distributed algorithms. Topics will include: (1) Perron Frobenius theory, (2) graph theory and algebraic graph theory, (3) basic network models such as averaging dynamics in discrete and continuous time, compartmental flow and positive systems, (4) stability theory for nonlinear systems, (5) Lotka-Volterra population dynamics, virus propagation dynamics, and coupled-oscillators dynamics, (6) examples are drawn from socio-economic networks, power grids, robotics.