Syllabus

Signal and system norms, computing H2 and H8 norms. [6Hrs]
Passivity and small gain theorems. [3Hrs]
Feedback interconnection, well-posedness. [4Hrs]
Parameter uncertainty linear fractional transformation, H8 conditions. [4Hrs]
Bounded Real Lemma, Riccati equation solution [6Hrs]
H8 control using state and output information. [6Hrs]
H8 controller synthesis solving Linear matrix inequality constraints. [2Hrs]
µ-synthesis, mixed sensitivity design.[3Hrs]
(if time permits).
Some Case studies.[2Hrs]
H8 loop shaping [2Hrs]

To understand signal norms, system norms and their effectiveness to quantify robustness in a linear system.

To get acquainted with the Riccati equation, inequality, and the LMI framework

To understand different methods of robust controller synthesis.

At the end of the course, students will be able

CO-I. To calculate signal and systems norms (H2 and H-infty).
CO-II. To formulate and guarantee feedback connection stability, robustness and well-posedness.
CO-III. To formulate and solve the Riccati equation.
CO-IV. To formulate and solve robust control problems.
CO-V. To represent problems in the LMI framework.
CO-VI. To use computational tools e.g. Matlab Toolbox, CVX, SeDuMi to solve robust control problems.

K. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice Hall , 1996

J. C. Doyle, B. A. Francis, A. R. Tannenbaum, Feedback Control Theory, Dover , 2009

M. Green, D.E. Johnson and D.J. N. Limebeer, Linear Robust Control, Prentice Hall , 2007

Geir E. Dullerud , Fernando Paganini, A Course in Robust Control Theory: A Convex Approach, Springer , 2001