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arXiv · 0707.0230

Positive Forms and Stability of Linear Time-Delay Systems

Matthew M. Peet·Antonis Papachristodoulou·Sanjay Lall
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Abstract

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 parametrization 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.

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Matthew M. Peet, Antonis Papachristodoulou, Sanjay Lall. 2007-07-02. Positive Forms and Stability of Linear Time-Delay Systems. https://arxiv.org/abs/0707.0230

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