Positive Forms and Stability of Linear Time-Delay Systems
- M. Peet, A. Papachristodoulou and S. Lall.
- SIAM Journal on Control and Optimization, V. 47, No. 6, p. 3237-3258, 2009.
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions. We give an explicit parameterization of a sequence of finite-dimensional subsets of the cone of positive Lyapunov functions using positive semidefinite matrices. This allows stability analysis of linear time-delay systems to be formulated as a semidefinite program.