Lyapunov stability tests for linear time-delay systems

An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proofs are presented in details for the case of systems with multiple delays. The state of the art, ongoing research and potential extensions to other classes of delay systems are discussed.

Automated summary

The paper provides an overview of stability conditions for time-delay systems using the Lyapunov matrix. It presents detailed results and proofs for systems with multiple delays. The state of the art, ongoing research, and potential extensions to other classes of delay systems are discussed.