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## CourseDetail

Degree
Master
Standard Academic Year
2nd year of master
Course delivery methods
face-to-face
Subject
Engineering & technology
Program
School
Grenoble INP Institute of Engineering Univ. Grenoble Alpes
Department
Campus
Grenoble - Polygone scientifique
Classroom
Course Offering Year
Course Offering Month
-
Weekday and Period
Capacity
Credits
5
Language
Course Number

### Non Linear and Robust Controls Université Grenoble Alpes

#### Course Overview

ROBUST CONTROL COURSE

Introduction
Industrial examples (automotive and electromechanical applications).
1 Tools
Hinf norm: how to de ne the gain of a MIMO system ?
Singular values of a transfer matrix, introduction to H2 and H1 norms.
Example of a mass/srping/damper system.
Internal stability: Notion of well-posedness, Small Gain theorem
2 Performance analysis
 De nition of the sensitivity functions
 frequency-domain performance indices (sensitivity functions, stability and robustness margins, bandwidth, SISO and MIMO cases)
3 Hinf control design
Performance Speci cations: selection of weighting functions.
Loop-shaping Mixed sensitivity problem.
Solving the Hinf control problem:  Obtaining the General control con guration
 Hinf controller structure (state feedback, dynamic output feedback)
 Problem solution using Riccati equations or LMIs -Bounded Real Lemma)
 Illustrative examples
4 Uncertainty and robustness
Representing uncertainties: unmodelled dynamics, frequency forms, unstructured uncertainties
Parametric uncertainties, LFT forms, structured uncertainties
Robust stability analysis: M structure, small gain theorem
Robust stability for unstructured uncertainties.
Robust performance analysis: A simpli ed Hinf criterion,
Introduction to mu-analysis - structured uncertainties

5 Introduction to LMIs
What is an Linear Matrix Inequality ? Brief optimisa-
tion background, De nition
Stability issue: From Lyapunov equation to LMIs
Control design: problem formulation: Example on
State feedback
6 Short introduction to LPV systems
De nition of Linear Parameter Varying systems, stability issue, control design
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http://ense3.grenoble-inp.fr/en/academics/non-linear-and-robust-controls-5eus5cnl

#### Learning Achievement

Ability for design and analysis of Hinfinity controlllers, robustness analysis, and the limits of the linearization, the analytical tools for nonlinear stability, and the basic principles of feedback control nonlinear state.

#### Competence

Ability for design and analysis of Hinfinity controlllers, robustness analysis, and the limits of the linearization, the analytical tools for nonlinear stability, and the basic principles of feedback control nonlinear state.

#### Course prerequisites

Linear Systems, Transfer and state space approach, frequency and time-domain analysis

#### Grading Philosophy

Exam
Homework
Project reports
Individual evaluation in Matlab tutorials

Lecture

Olivier Sename

#### Other information

Course content can evolve at any time before the start of the course. It is strongly recommended to discuss with the course contact about the detailed program.

Please consider the following deadlines for inbound mobility to Grenoble:
- April 1st, 2020 for Full Year (September to June) and Fall Semester (September to January) intake ;
- September 1st, 2020 for Spring Semester intake (February – June).

#### Site for Inquiry

Please inquire about the courses at the address below.

Contact person: international.cic_tsukuba@grenoble-inp.fr