The linear matrix inequalities (LMIs) have been regareded as a powerful tool for various control problems as a number of efficient algorithms such as ellipsoid method and interior point method have been developed. In this sense, this course studies the mathematical fundamentals of LMIs by using the aruguments on convex optimization. Furthermore, this course provides solutions for control problems with respect to minimizing various system norms. Students will understand mathematical basis for LMI as well as its related solution procedures for the control problems. The problems introduced in this course are closely related with the recent academic trends in the control community, I.e., multi-objective control, and are intended to strengthen understanding of the analysis and synthesis of linear control systems.

Linear Systems Theory(EECE 564)

Exam(60%)+Homework(30%)+Attendance(10%)

The instructor will provide lecture notes on schedule. There is an additional reference strongly recommended and possibly available online as follows.
C. Scherer and S. Weiland, Linear Matrix Inequalities in Control

In this course, the instructor emphasizes mathematical basis for linear matrix inequalities with their applications to multi-objective control problems. The course material will include

● Convex optimization and linear matrix inequalities
● Dissipative dynamical systems
● A classification of storage functions
● Lyapunov stability and nominal performances
● Single-objective synthesis
● Multi-objective synthesis
● Elimination of parameters
● State-feedback problems
● Robust stability and performance

In a case of online course, the lecture videos will be provided.