Tutorial on Lyapunov-based methods for time-delay systems. (English) Zbl 1403.93158
Summary: Time-delay naturally appears in many control systems, and it is frequently a source of instability. However, for some systems, the presence of delay can have a stabilizing effect. Therefore, stability and control of time-delay systems is of theoretical and practical importance. Modern control systems usually employ digital technology for controller implementation, i.e. sampled-data control. A time-delay approach to sampled-data control, where the system is modeled as a continuous-time system with the delayed input/output became popular in the networked control systems, where the plant and the controller exchange data via communication network. In the present tutorial, introduction to Lyapunov-based methods for stability of time-delay systems is given together with some advanced results on the topic.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C57 | Sampled-data control/observation systems |
| 93C05 | Linear systems in control theory |
| 93C10 | Nonlinear systems in control theory |
| 93D25 | Input-output approaches in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
Keywords:
time-delay systems; stability; Lyapunov method; input-output stability; sampled-data systemsReferences:
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