Reducing the computational cost of the sum-of-squares stability test for time-delayed systems

Abstract

This paper considers the problem of reducing the computational complexity associated with the Sum-of-Squares approach to stability analysis of time-delay systems. Specifically, this paper considers systems with a large state-space but with relatively few delays—the most common situation in practice. The paper uses the general framework of coupled differential-difference equations with delays in low-dimensional feedback channels. This framework includes both the standard delayed and neutral-type systems. The approach is based on recent results which introduced a new type of Lyapunov-Krasovskii form which was shown to be necessary and sufficient for stability of this class of systems. This paper shows how exploiting the structure of the new functional can yield dramatic improvements in computational complexity. Numerical examples are given to illustrate this improvement.