Contraction Analysis of Time-Delay Systems
Provides a theoretical foundation for analyzing incremental stability in time-delay systems, which is important for control engineers working with delayed dynamics.
This paper extends contraction analysis to nonlinear time-delay systems by developing differential Lyapunov-Krasovskii and Lyapunov-Razumikhin frameworks, proving that their existence guarantees uniform incremental exponential stability. The results are applied to stabilizing feedback control design via linear matrix inequalities.
In this paper, we investigate contraction analysis for nonlinear time-delay systems described by functional differential equations. We first extend the concept of Lyapunov-Krasovskii functionals within the differential framework. We then show that its existence is equivalent to that of an incremental Lyapunov-Krasovskii functional and guarantees uniform incremental exponential stability. Next, we extend the concept of Lyapunov-Razumikhin functions within the differential framework, whose existence also ensures uniform incremental exponential stability. As an application of our results, we formulate stabilizing feedback control design for nonlinear time-delay systems with single delays in terms of linear matrix inequalities.