The concept of robustness plays an important role in systems design. A system is said to be robust if it is possible to guarantee its correct dynamic behaviour on the basis of its mathematical model, despite imperfections in the model, variations in its characteristics during manufacture, variations in the environment or ageing. The quest for robustness has led to the introduction of feedback loops in systems, which have the major advantage of ensuring that the overall behaviour of the system remains invariant despite wide variations in its components. This remarkable property is exploited intensively in Automatic Control for the design of control systems. Although this property began to be exploited a few decades ago, it is only recently that quantitative tools have been developed, taking advantage of the development of computer processing power and recent advances in Optimisation, particularly under LMI constraints. The aim of this course is to present the analysis of uncertainties, both structured and unstructured, with illustrations on the design of systems but also on their analysis, i.e. on the validation of specifications for a system. The development of this approach is in line with current industrial requirements for finding the best possible compromise in a specification. It also provides an introduction to convex optimisation, which has become an important numerical tool in Automatic Control in recent years.
● Robustness of dynamical systems
● Robustness and feedback
● Convex optimization for engineers
● Efficient optimization for robustness: analysis and design
● Case studies