Course Title : Modern Control Theory

Code 90580
Course Year 3rd year
Term 2nd term
Class day & Period
Credits 2
Restriction No Restriction
Lecture Form(s) Lecture

Course Description

This course provides the fundamentals in modern control theory - centered around the so-called state space methods - as a continuation of classical control theory taught in Linear Control Theory. Emphasis is placed on the treatment of such concepts as controllability and observability, pole allocation, the realization problem, observers, and linear quadratic optimal regulators.


The grading is based on the evaluation of reports and final examination.

Course Goals

The objective is to study controllability and observability that are the basis of modern control theory, and also understand design methods such as optimal regulators. It is hoped that the course provides a basis for a more advanced topic such as robust control theory.

Course Topics

Theme Class number of times Description
Overview of modern control theory 1 We review the history of control, and the historical background of how and why modern control theory has been developed. The importance, effectiveness and characteristics of this theory will also be discussed.
State space model and linear dynamical system 2 We discuss some fundamental properties of systems described by state space equations. In particular, basic properties of linear dynamical systems and system equivalence are also discussed.
Controllability and observability 3 We introduce the fundamental notions of controllability and observability for linear dynamical systems, and also discuss their basic properties and their criteria.
Canonical decomposition 1 We give the canonical decomposition for linear systems, and investigate its relationship with controllability, observability, and pole allocation.
Realization problem 2 We introduce the realization problem that constructs state space representations from transfer functions for single-input and single-output systems.
State feedback and dynamic compensators 3 We introduce the construction of dynamic compensators via state feedback, pole allocation and observers. The relationships with controllability and observablity are also discussed.
Opimal regulators 3 We give the basic construction of optimal regulators, in particular, the introduction of the matrix Riccati equation, its solvability, relationship to stability and observability, and root loci.
Final check of students' achievement 1 Final examination.


None specified.


Linear Algebra, K. Jaenich, translation by M. Nagata, Gendai-suugakusha,
Mathematics for Systems and Control, Y. Yamamoto, Asakura,


It is desirable that the student has studied classical control theory (linear control theory). Fundamental knowledge on linear algebra is assumed, e.g., matrices, determinants, rank of a matrix, dimension of a vector space, isomorphism.

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