Positive Forms and Stability of Linear Time-Delay Systems
- M. Peet, A. Papachristodoulou and S. Lall.
- Proceedings of the IEEE Conference on Decision and Control, p. 187--193, 2006.
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that stability implies that there exists a quadratic Lyapunov function on the state space, although this is in general infinite dimensional. We give an explicit parametrization of a finite-dimensional subset of the cone of Lyapunov functions. Positivity of this class of functions is enforced using sum-of-squares polynomial matrices. This allows the computation to be formulated as a semidefinite program.