# Welcome to SYSOS

### From SYSOS

# SYSOS: Systems using Sum of Squares

We develop tools and algorithms for the scalable analysis of nonlinear system descriptions and the design of control laws using computational tools based on the Sum of Squares decomposition and Semidefinite Programming. In particular, our group concentrates on:

- Nonlinear systems analysis, Sum of Squares optimization and Lyapunov techniques. In this spirit, we have developed methods for stability analysis of systems described by Ordinary, Delay and Partial Differential Equations, with applications in Systems Biology, Population Dynamics and Engineering.

- Software Development (SOSTOOLS). This can be found here. A new version is currently under development and more examples will be added soon.

- Large-scale Networked Systems analysis with communication and structural constraints. Examples in this field come from synchronization phenomena in oscillator Networks with applications to Kuramoto couplings and synchronization of cardiac cells and Network Congestion Control for the Internet. We are looking at multi-agent systems consensus under communication and structural constraints such as the effect of time delays and switching topologies.

- Fluid mechanics and Heat transfer, from a control perspective. We are taking a control engineering approach to understand questions in Hydrodynamic Stability and mechanisms for background noise energy amplification and subsequent reduction.

## Support

## Members

- Mr Bence Melykuti

- Mr Yo-Cheng (Mark) Chang