Delayed systems
• Examples of time-delay systems.
• Basic control design: Ziegler and Nichols, Smith's predictor, Tsypkin's theorem.
• Models and approaches: Convolution systems, transfers, systems over a ring, D systems, realization theory.
• Stability: Exponential, L1, L2, and BIBO-stability, zeros of quasipolynomials, robust stability, D-partition.
• Stabilization: Static feedback, Robust stabilisation, Prediction and pole placement.
• Examples of control design: Logistic system, cyber-physical system, systems over a network.
Chaotic systems
• Introduction to chaotic systems: definitions, examples
• Analysis of chaotic systems:
• Fixed and periodic points, attractive and repulsive orbits, chaotic attractors. General eigenvalues-based rules for continuous-time and discrete-time systems
• Local and global bifurcations; bifurcation cascades and roads to chaos
• Lyapunov exponents for evaluating chaoticity
• Bassins of attraction and multistability
• Synchronization of chaotic systems using observers
• Applications: Chaos control, encryption and design of chaotic pseudo-random number generators