Course title
6M019300,7M9917001
Course content
The approach based on linear matrix inequality (LMI) is now an important tool in analysis and design of modern control. We will first review some basic modern control theory, and then learn from convex sets, convex functions and 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. Students can understand basic modern control theory, master the definition of convex sets, convex functions and apply basic idea of convex programming.
2. Students can understand the definition and properties of LMIs, and perform basic simulation for solving LMIs.
3. Students can derive and solve LMIs for 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
Review of differential equations together with simple mechanical systems and RCLs 190minutes
3． Solutions of SSR Review of differential equations and Laplace transform 190minutes
4． Stability of control systems Eigenvalues of matrices and system responses (trajectories) 190minutes
5． Robustness and robust stability of control systems Review norm of vectors and matrices 190minutes
6． Review and Report 1 (system modeling, solution
and stability)
Review of Week 1-5 190minutes
7． Convex sets, convex functions, convex
programming
Review of functions with one or two variables 190minutes
8． Definition and properties of LMIs Review positive (negative) definite properties of symmetric matrices 190minutes
9． Stability analysis with LMIs Review stability concept and system behavior 190minutes
10． Robust stability analysis with LMIs Preview of system uncertainty and its evaluation 190minutes
11． LMI based stabilization via state feedback Review the basic idea of state feedback in control systems 190minutes
12． LMI based robust stabilization via state
feedback (polytopic uncertainties)
Review of convex functions and the definition of polytopic
uncertainties with convex sets
190minutes
13． LMI based robust stabilization via state
feedback (norm-bounded uncertainties)
Preview of the definition of bounded uncertainties with matrix norms 190minutes
14． Review and Report 2 Review of the whole course 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Report 1 Report 2 Total.
1. 30% 10% 40%
2. 30% 30%
3. 30% 30%
Total. 30% 70% -
Evaluation method and criteria
Report 1: 30%
Report 2: 70%
-------------------
PASS when reaching 60% of the whole evaluation
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
No text books; Will deliver handouts and suggest several reference books

【1】Katsuhiko Ogata: Modern Control Engineering (5th edition), Prentice Hall, 2010

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

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

【4】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
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 problem-solving skills
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
Applicable Used some of the knowledge and theory with simulation in analysis and design of real plants
Education related SDGs:the Sustainable Development Goals
• 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
• 11.SUSTAINABLE CITIES AND COMMUNITIES
• 12.RESPONSIBLE CONSUMPTION & PRODUCTION
• 13.CLIMATE ACTION