Fridman E. Introduction to Time-Delay Systems: Analysis and Control

Springer International Publishing, Switzerland, 2014. — 378 p. — (Systems & Control: Foundations & Applications) — ISBN: 9783319093925.Time-delay often appears in many real-world engineering systems either in the state, the control input, or the measurements. Delays are strongly involved in challenging areas of communication and information technologies: in stabilization of networked controlled systems and in high-speed communication networks. Time-delay is, in many cases, a source of instability. However, for some systems, the presence of delay can have a stabilizing effect. The stability analysis and robust control of timedelay systems (TDSs) are, therefore, of theoretical and practical importance.
As in systems without delay, an efficient method for stability analysis of TDSs is the Lyapunov method. For TDSs, there exist two main Lyapunov methods: the Krasovskii method of Lyapunov functionals (1956) and the Razumikhin method of Lyapunov functions (1956). The Krasovskii method is applicable to a wider range of problems and it leads usually to less conservative results, than the Razumikhin method.LinearTDSs
Lyapunov-Based Stability Analysis
Performance Analysis of TDSs
Control Design for TDSs
Discrete-Time Delay Systems
Sampled-Data and NCSs: A Time-Delay Approach