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    GRADUATE SCHOOL

    Ph.D. In Electrical-Electronics Engineering

    EEE 611 | Course Introduction and Application Information

    Course Name
    Nonlinear System Analysis
    Code
    Semester
    Theory
    (hour/week)
    Application/Lab
    (hour/week)
    Local Credits
    ECTS
    EEE 611
    Fall/Spring
    3
    0
    3
    7.5

    Prerequisites
    None
    Course Language
    English
    Course Type
    Elective
    Course Level
    Third Cycle
    Mode of Delivery -
    Teaching Methods and Techniques of the Course -
    National Occupation Classification -
    Course Coordinator
    Course Lecturer(s)
    Assistant(s) -
    Course Objectives The course aims the students: i) to get a solid mathematical background on nonlinear systems’ equilibrium points, limit cycle and other nonlinear behaviors together with their Liapunov and input-output stabilities, ii) to gain skills of determining the existence, qualitative properties and stability of certain nonlinear behaviors for a given nonlinear system and iii) to have a nonlinear systems point of view.
    Learning Outcomes

    The students who succeeded in this course;

    • Find equilibrium point(s) and limilt cycles of nonlinear systems
    • Linearize a nonlinear system to prove the Liapunov local stability of equilibrium point or a trajectory of a nonlinear system and decide the Liapunov stability in terms of eigenvalues of the Jacobian matrix.
    • Determine the bounded-input bounded-output stability of a nonlinear system.
    • Derive Liapunov function to prove the Liapunov stability of equilibrium point or a trajectory of a nonlinear system
    Course Description Introduction to nonlinear phenomena: multiple equilibria, limit cycles, bifurcations, complex dynamical behavior. Planar dynamical systems, analysis using phase plane techniques. Describing functions. Input-output analysis and stability. Lyapunov stability theory. The Lure problem, Circle and Popov criterion. Feedback linearization and sliding mode control.

     



    Course Category

    		Core Courses
    X
    Major Area Courses
    Supportive Courses
    Media and Management Skills Courses
    Transferable Skill Courses

     

    WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

    Week Subjects Related Preparation Learning Outcome
    1 Examples for nonlinear systems. Derivation of state equations of nonlinear circuits and control systems. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    2 Equilibrium point, fixed point, multiple equilibria, existence and uniqueness of equilibrium points and fixed points. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    3 Existence and uniqueness of solutions to nonlinear state equations. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    4 Existence and uniqueness of nonlinear difference equations, nonexpansion mapping, contraction mapping, implicit and inverse function theorems. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    5 Phase portraits for second order dynamical systems, existence of periodical solutions, Poincare-Bendixson Theorem M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    6 Liapunov stability and asymptotical stability of an equilibrium point of a nonlinear system, Liapunov’s first method for stability. Hartman-Grobman Theorem M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    7 Liapunov’s second method. Liapunov functions for linear and nonlinear, time-invariant and time-varying systems. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    8 Lasalle’s Invariance Theorem. Necessary conditions for Liapunov stability. Complete stability. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    9 1. Midterm
    10 Control problems as Liapunov stability problems. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    11 Bounded-Input Bounded-Output stability for nonlinear systems. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    12 Lure’s system. Aizerman’s conjecture. Sector conditions. Circle criteria. Popov criteria, M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    13 2. Midterm
    14 State feedback linearization, output feedback linearization. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    15 Sliding mode control, strict feedback control. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition, SIAM, 2002 Hassan K. Khalil, Nonlinear Systems, 3nd Edition, Printice Hall, 2001
    16 Review of the Semester  

     

    Course Notes/Textbooks The textbook referenced above and lecture notes
    Suggested Readings/Materials Related Books

     

    EVALUATION SYSTEM

    Semester Activities Number Weigthing
    Participation
    Laboratory / Application
    Field Work
    Quizzes / Studio Critiques
    Portfolio
    Homework / Assignments
    5
    20
    Presentation / Jury
    Project
    Seminar / Workshop
    Oral Exams
    Midterm
    2
    40
    Final Exam
    1
    40
    Total

    Weighting of Semester Activities on the Final Grade
    7
    60
    Weighting of End-of-Semester Activities on the Final Grade
    1
    40
    Total

    ECTS / WORKLOAD TABLE

    Semester Activities Number Duration (Hours) Workload
    Theoretical Course Hours
    (Including exam week: 16 x total hours)
    16
    3
    48
    Laboratory / Application Hours
    (Including exam week: '.16.' x total hours)
    16
    0
    Study Hours Out of Class
    15
    4
    60
    Field Work
    0
    Quizzes / Studio Critiques
    0
    Portfolio
    0
    Homework / Assignments
    5
    12
    60
    Presentation / Jury
    0
    Project
    0
    Seminar / Workshop
    0
    Oral Exam
    0
    Midterms
    2
    15
    30
    Final Exam
    1
    27
    27
        Total
    225

     

    COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

    #
    		 PC Sub Program Competencies/Outcomes
    * Contribution Level
    1
    2
    3
    4
    5
    1 Accesses information in breadth and depth by conducting scientific research in Electrical and Electronics Engineering; evaluates, interprets and applies information.
    -
    -
    -
    -
    X
    2 Is well-informed about contemporary techniques and methods used in Electrical and Electronics Engineering and their limitations.
    -
    -
    X
    -
    -
    3 Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines. Knows and applies the research methods in studies of the area with a high level of skill.
    -
    X
    -
    -
    -
    4 Is informed about new and upcoming applications in the field and learns them whenever necessary.
    -
    -
    X
    -
    -
    5 Defines and formulates problems related to Electrical and Electronics Engineering, develops methods to solve them and uses progressive methods in solutions. Can independently realize novel studies that bring innovation to the field, or methods, or design, or known methods.
    -
    -
    -
    -
    X
    6 Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.
    -
    -
    -
    X
    -
    7 Designs and implements studies based on theory, experiments and modeling; analyses and resolves the complex problems that arise in this process. Performs critical analysis, synthesis and evaluation of new and complex ideas.
    -
    -
    -
    -
    X
    8 Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility.
    -
    X
    -
    -
    -
    9 Engages in written and oral communication at least in Level C1 of the European Language Portfolio Global Scale.
    -
    -
    X
    -
    -
    10 Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.
    X
    -
    -
    -
    -
    11 Evaluates the results of scientific, technological and engineering research and development activities in terms of the social, environmental, health, safety and legal aspects. Examines social relations and norms related to the field, and develops and makes attempts to change them if necessary. Knows their project management and business applications, and is aware of their limitations in Electrical and Electronics Engineering applications.
    X
    -
    -
    -
    -
    12 Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. Adheres to the principles of research and publication ethics.
    X
    -
    -
    -
    -

    *1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

     

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