Course title
6M017600,7M9905001
Course content
The approach based on linear matrix inequality (LMI) is now an important tool in analysis and design of modern control. We will learn from convex sets, convex functions and then proceed to definition of LMIs in control theory. Thereafter, we present the system analysis (focusing on stability) and design (focusing on stabilization and robustness) with LMIs. Numerical simulations are also described and practiced in MATLAB and Simulink.
Purpose of class
The approach based on linear matrix inequality (LMI) is now an important tool in analysis and design of modern control. We will learn from convex sets, convex functions and then proceed to definition of LMIs in control theory. Thereafter, we present the system analysis (focusing on stability) and design (focusing on stabilization and robustness) with LMIs. Numerical simulations are also described and practiced in MATLAB and Simulink.
Goals and objectives
1. Can understand convex sets, convex functions and basic idea of convex programming
2. Can understand the definition and properties of LMIs, together with basic simulation for solving LMIs
3. Can understand the idea and procedure of using LMIs in analysis and design of modern control systems
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Course guidance, history of LMIs in modern control theory Comparison between classic and modern control 190minutes
2． State space representation (SSR) of modern control systems, Solutions of SSR Review of differential equations, Laplace transform 190minutes
3． Stability and and robust stability of control systems Review eigenvalues of matrices and system response (trajectory); Review norm of vectors and matrices 190minutes
4． Convex sets, convex functions, convex programming; Review and Report 1 (system modeling, solution and stability) Review Week 1-3, convex sets and convex function in calculus 190minutes
5． Definition and properties of LMIs, Stability analysis with LMIs Review positive (negative) definite properties of symmetric matrices; Review stability concept and system behavior 190minutes
6． Robust stability analysis with LMIs; LMI based stabilization via state feedback Review the basic idea of state feedback in control systems 190minutes
7． LMI based robust stabilization via state feedback (polytopic uncertainties) ; Review and Report 2 Try to understand system uncertainty and how to evaluate uncertainty; Review of the whole course 190minutes
8． None None 0minutes
9． None None 0minutes
10． None None 0minutes
11． None None 0minutes
12． None None 0minutes
13． None None 0minutes
14． None None 0minutes
Total. - - 1330minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Report 1 Report 2 Total.
1. 40% 40%
2. 30% 30%
3. 30% 30%
Total. 40% 60% -
Evaluation method and criteria
Report 1: 40%
Report 2: 60%
-------------------
PASS when reaching 60% of the whole evaluation, or in other words, understanding how to use and solve LMIs in stability analysis and stabilization with state feedback.
Textbooks and reference materials
No text books; Will deliver handouts and suggest several reference books

【1】岩崎徹也：ＬＭＩと制御，昭晃堂，1997 (ISBN 4785690534)

【2】Boyd, Vandenberghe: Convex Optimization, Cambridge University Press, 2004
(http://www.stanford.edu/~boyd/cvxbook/) (ISBN 978-0-521-83378-3)

【3】Boyd, El Ghaoui, Feron, Balakrishnan: Linear Matrix Inequalities in System and Control Theory, SIAM, 1994 (http://www.stanford.edu/~boyd/lmibook/lmibook.pdf)
(ISBN 0-89871-334-X)

Prerequisites
Desirable to have basic knowledge of calculus and linear algebra
Office hours and How to contact professors for questions
• 12:30--13:00 every Monday
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
• Course that cultivates an ability for utilizing knowledge
• Course that cultivates a basic self-management skills
• Course that cultivates a basic problem-solving skills
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals