Robust H-infinity Control

Course Name: Robust H-infinity Control

Course No.: ECE 1124021

Teacher: Prof. Hamid D. Taghirad

Taught Semesters: Fall (2017, 2015, 2012, 2011, 2009, 2007, 2005, 2004, 2002)

Tentative Course Timetable

The tentative course contents are as following:

Time: Teaching Contents
Week 1 Introduction: Modeling, uncertainty and robustness, Sensitivity function, general regulator problem, Small-gain theorem and H-infinity control.
Week 2 Norms: Norms of signals, Norms of systems, Relation between signals and systems norm, Computing 2 and ∞ norms, Multivariable norms, Hilbert and Banach spaces.
Week 3 Robust problems Modeling: Plant uncertainty, different types of uncertainty, parametric uncertainty, unstructured uncertainty, illustrative examples.
Week 4 Robust problems Analysis:  Internal stability, Robust stability, based on Sensitivity functions, Hnorms, and structured singular values.
Week 5 Robust controller synthesis:  Controller parameterization, Design constraints, algebraic constraints, analytic constraints, interpolation conditions, waterbed effect.
Week 6 Mixed Sensitivity Problem:  Definition to mixed sensitivity, the augmented state-space model.
Week 7 Solution to general regulator problem (Methods): H2, H solutions based on Ricatti Equations. H solutions based on LMI, H2/ H solutions.
Week 8 Solution to general regulator problem (Methods): H solutions based on LMI, H2/ H solutions.
Week 9 Midterm Exam
Week 10 Solution to general regulator problem (implementations): Design for SISO and Non-minimum phase, Comprehensive case study.
Week 11 Solution to general regulator problem (implementations): Design for unstable and Non-minimum phase systems and disturbance rejection, Comprehensive case study.
Week 12 μ Analysis: Structured singular values,  μ -Analysis.
Week 13 μ synthesis:  μ -Synthesis, Comprehensive case studies.
Week 14 Case studies: Control of F14 Aircraft, robust problem formulation, controller synthesis, performance evaluation and improvement.
Week 15 Case studies: Three inertia system: robust modeling and identification, weighting function selection, H and H2/ H controller design and improvement, μ synthesis, controllers performance evaluations.

Course Content



1 Hamid D. Taghirad, M. Fathi, F. Zamani O., “Robust H-infinity Control”, K. N. Toosi University of Technology Publication, 3rd Ed. 2018.
2 Doyle, Francis, Tannenbaum, “Feedback Control Theory” ,Macmillan Publishing, 1990 .
3 Zhou K., with  J. Doyle, “Essentials of Robust Control”, Prentice Hall, 1998.
4 Skogestad S. and I. Postlethwaite “Multivariable Feedback Control”, John Wiley & Sons, 1996.
5. G.E. Dullerud and F. Paganini, “A course in Robust Control Theory: A convex Approach” , Springer Verlag, 1991.