# Department of Electrical and Electronics Engineering

Course Details

#### ELE701 - Linear System Theory

2023-2024 Spring term information
The course is not open this term
ELE701 - Linear System Theory
 Program Theoretýcal hours Practical hours Local credit ECTS credit PhD 3 0 3 10
 Obligation : Elective Prerequisite courses : - Concurrent courses : - Delivery modes : Face-to-Face Learning and teaching strategies : Lecture, Question and Answer, Problem Solving Course objective : Many engineering problems can be analyzed and solved within the framework of system concept, which is a very fundamental notion in engineering. It is possible to classify systems into two main groups as liner and nonlinear although they may have many different properties and characteristics. Systems can be assumed as linear under certain conditions despite the fact that most of the systems are nonlinear. In this way, linear systems point of view can also be used in the analysis of nonlinear systems. In this course, the aim is to provide the necessary background for the students to be able to understand and solve the engineering problems by using the theory and methods developed for linear systems. Learning outcomes : A student completing the course successfully is expected to understand the system concept. be able to obtain linear models for physical systems. be aware of diferences and discrepancies between the actual system and its linear model. fully understand and analyse such systems. have the adequate knowledge to follow further studies involving system concept. Course content : Linear spaces. Change of basis. Linear operators. Range space and null space. Eigenvalues and eigenvectors. Jordan form representation. Function of a square matrix. Norms. Linear system description: input-output and state variable descriptions, time invariant and time varying systems. Modal decomposition. Equivalent (or similar) systems and equivalence (or similarity) transformation. Linear system analysis: controllability, observability and stability. References : 1. Chen C.T., Linear System Theory and Design, HRW, 1984.; 2. Kailath T., Linear Systems, Prentice Hall, 1980.; 3. Decarlo R.A., Linear Systems: A state variable approach with numerical; implementation, Prentice Hall, 1989.; 4. Rugh W.J., Linear System Theory, 2nd Ed., Prentice Hall, 1996.; 5. Brogan W.L., Modern Control Theory, 3rd Ed., Prentice Hall, 1991.
Course Outline Weekly
Weeks Topics
1 Linear spaces : field, linear space, subspace, span, linear independence, dimension, basis, change of basis.
2 Linear oprerators and representations of a linear operator.
3 Linear operators: range and null spaces, eigenvalues and eigenvectors, Jordan form representation.
4 Polynomial of a square matrix, minimal polynomial, function of a square matrix, norms and inner product.
5 Linear system description: input-output approach (for both time-invariant and time varying).
6 Linear system description: state variable approach (for both time-invariant and time varying).
7 Solution of dynamical equations, fundamental martix and state transition matrix.
8 Solution of dynamical equation, computation of eAt and (SI-A)-1, Faddeev algorithm, modal decomposition.
9 Equivalent (or similar) systems and equivalence (or similarity) transformation.
10 Midterm Exam
11 Linear system analysis: Controllability and observability.
12 Linear system analysis: Controllability and observability.
13 Linear system analysis: Stability.
14 Linear system analysis: Stability.
15 Final exam
16 Final exam
Assessment Methods
Course activities Number Percentage
Attendance 0 0
Laboratory 0 0
Application 0 0
Field activities 0 0
Specific practical training 0 0
Assignments 6 10
Presentation 0 0
Project 0 0
Seminar 0 0
Quiz 0 0
Midterms 1 40
Final exam 1 50
Total 100
Percentage of semester activities contributing grade success 50
Percentage of final exam contributing grade success 50
Total 100
Course activities Number Duration (hours) Total workload
Course Duration 13 3 39
Laboratory 0 0 0
Application 0 0 0
Specific practical training 0 0 0
Field activities 0 0 0
Study Hours Out of Class (Preliminary work, reinforcement, etc.) 14 9 126
Presentation / Seminar Preparation 0 0 0
Project 0 0 0
Homework assignment 6 6 36
Quiz 0 0 0
Midterms (Study duration) 1 25 25
Final Exam (Study duration) 1 30 30