Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

Person Responsible for Information Package

Linear System Theory I

Course Code	: EEE501
Course Type	: Required
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 8

Objectives of the Course

System concept having great importannce in engineering sciences is studied in two titles as linear systems and nonlinear systems. Although systems in nature generally exhibit nonlinear behavior, since they can be linearized under some conditions and for some regions by some approximations, theory of linear systems have great importance. In this manner, nonlinear systems frequently observed in nature can be solved by the point of linear system theory. In this respect, theory of linear systems is being studied in this course.

Course Content

Mathematical description of systems; linear and nonlinear systems; linearization; Linear Time Invariant (LTI) and Linear Time Varying (LTV) systems; continuous-time and discrete-time systems; state-space equations and solutions of linear systems; linear algebra; canonic forms; stability, controllability and observability of systems and applications to linear systems.

Name of Lecturer(s)

Prof. Yılmaz KALKAN

Learning Outcomes

1.	To learn the classification, nature, and concepts of systems and be able to do the mathematical description of systems.
2.	To be able to linearize nonlinear systems.
3.	To acquire the required linear algebra concepts, applications, and skills required for the linear system theory.
4.	To learn the theory of linear systems and be able to apply to the systems.
5.	To improve understandings in analyses and engineering design of systems.

Recommended or Required Reading

1.	Chen C.T., Linear System Theory and Design, HRW, 1984.
2.	G. Strang, Linear Algebra and its Applications, 4th Ed. Brooks/Cole, 2006.
3.	Kailath T., Linear Systems, Prentice Hall, 1980.
4.	C.A. Desoer, Notes for a Second Course on Linear Systems, Van Nostrand Reinhold, 1970.
5.	S. Axler, Linear Algebra Done Right, Springer, 1997.
6.	Decarlo R.A., Linear Systems: A state variable approach with numerical implementation, Prentice Hall, 1989.

Weekly Detailed Course Contents

Week 1 - Theoretical

Mathematical description of systems: Causality, Linear and nonlinear systems, time independent and time dependent systems, state-space equations, linearization. Chen, Ch.1, Introduction & Ch.2

Week 2 - Theoretical

Mathematical description of systems (continuing): state-space equations of linear systems and transfer function, concepts of zero-input response and zero-state response, continuous-time and discrete-time systems, transformation of linear continuous systems to discrete systems, problem solutions and Matlab applications. Chen, Ch.2

Week 3 - Theoretical

Linear algebra: Basis, representation and orthonormalization, systems of linear equation systems and their solutions, linear independence. Chen, Ch.3

Week 4 - Theoretical

Linear algebra (continuing): Similarity transformations, rotation matrices and their applications. Chen, Ch.3

Week 5 - Theoretical

Linear algebra (continuing): Eigen values and eigenvectors, diagonal forms and Jordan forms. Chen, Ch.3

Week 6 - Theoretical

Linear algebra (continuing): Square matrix functions, Cayley-Hamilton theorem, Lyapunov equation. Chen, Ch.3

Week 7 - Theoretical

Linear algebra (continuing): Quadratic forms, positive definiteness, singular value decomposition, norm of matrices, problem solutions and applications. Chen, Ch.2

Week 8 - Theoretical

Repeat the all chapters - Midterm Exam

Week 9 - Theoretical

State-space equations and realization: Linear & Time Invariant (LTI) continuous systems and their solutions, state-space equations of LTI discrete systems and their solutions. Chen, Ch.4

Week 10 - Theoretical

State-space equations and realization (continuing): LTI equivalent systems, equivalent state-space equations of LTI systems and equality transformations. Chen, Ch.4

Week 11 - Theoretical

State-space equations and realization (continuing): Canonic forms in the LTI systems, magnitude scaling of Op-amp circuits, realizations. Chen, Ch.4

Week 12 - Theoretical

State-space equations and realization (continuing): Linear & Time Varying (LTV) continuous and discrete systems and their solutions, equivalent LTV systems and their transformations, time dependent realizations. Chen, Ch.4

Week 13 - Theoretical

Stability: Input-output stability of LTI systems, applications to the systems and problem solutions. Chen, Ch.5

Week 14 - Theoretical

Stability (continuing): Stability in LTV systems. Chen, Ch.5, Controllability and observability: controllability matrix, observability matrix, canonic decompositions, applications to the systems and problem solutions. Chen, Ch.6

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Midterm Examination	1	%30
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	10	3	182
Midterm Examination	1	5	3	8
Final Examination	1	7	3	10
TOTAL WORKLOAD (hours)				200

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7
OÇ-1	5	5	5	5	5	5	5
OÇ-2	5	5	5	5	5	5	5
OÇ-3	5	5	5	5	5	5	5
OÇ-4	5	5	5	5	5	5	5
OÇ-5	5	5	5	5	5	5	5

Person Responsible for Information Package