Prerequisites: Introduction to Modern Linear Control.
1. Models of systems with time-delay: networked-control systems, communication network mod-
els, models in biology.
2. Basic theory: solution concept and step method. Classi cation of systems with time-delay
(retarded, neutral type systems). Existence of solutions. Linear time-invariant systems with
delay: characteristic equation, solution of linear non-homogenous equations.
3. Stability analysis. Direct Lyapunov approach: Krasovskii and Razumikhim methods. An LMI
approach to stability: delay-independent/delay-dependent conditions . Exponential bounds
and L2-gain analysis. Stabilization by using delays and discretized Lyapunov functional.
Analysis of sampled-data and networked control systems. Input-to-state stability and control
under quantization. Switched time-delay systems.
4. Control design: predictor-based control, Smith predictor, LMI approach to robust stabiliza-
tion. Systems with saturated actuators. H1 control. Sliding mode control of systems with
delay. LQR problem and Kalman Filter.
5. An LMI approach to control of some distributed parameter systems.