2026 ABRO Course on Advances in Automatic Control
Linear Matrix Inequalities (LMIs) have become a central tool in modern systems and control theory thanks to their ability to cast a wide range of analysis and synthesis problems as tractable convex optimization programs. This PhD-level course provides a rigorous introduction to LMIs and their application to linear time-invariant (LTI) systems, beginning with fundamental concepts of LMI feasibility, Lyapunov stability analysis, and basic controller design. Building on these foundations, the course then extends the framework to robust control of systems affected by polytopic uncertainties and to gain-scheduled control design for linear parameter-varying (LPV) models. Additionally, the course will explore how LMIs naturally handle structural variations such as switched dynamics and time-delay systems. The second half of the course focuses on observer design through LMIs. Besides classical Luenberger observers, students learn how to formulate and synthesize unknown-input observers for fault detection and isolation, as well as interval observers capable of providing real-time, guaranteed state bounds under uncertainty, disturbance, and noise assumptions. The course concludes by examining emerging research directions, including data-driven LMI-based control design and the recently proposed concept of quadratic repulsiveness, highlighting new opportunities at the intersection of optimization, learning, estimation, and feedback control.
Venue: room A2 (Diag)
Schedule:
June 8 -- 14:00-17:00
June 9 -- 14:00-17:00
June 10 -- 14:00-17:00
June 11 -- 14:00-17:00
June 16 -- 10:00-13:00
June 17 -- 10:00-13:00
June 18 -- 10:00-12:00