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ISTANBUL GELİŞİM UNIVERSITY INFORMATION SYSTEM

LİNEER SİSTEM TEORİSİ I COURSE IDENTIFICATION AND APPLICATION INFORMATION

Code Name of the Course Unit Semester In-Class Hours (T+P) Credit ECTS Credit
EEM501 LİNEER SİSTEM TEORİSİ I 1 3 3 6

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week Preparatory Topics(Subjects) Method
1 - Outline and introduction -
2 - Review of Linear Algebra Concepts: Linear Spaces, Basis Vectors, Linear Transformations -
3 - Mathematical Background (Fields, Vector Spaces, Matrices, Matrix inverse, Metric Spaces, Norms, Normed Spaces, Inner Products, Inner Product Spaces, Completeness). -
4 - Mathematical Background (Fields, Vector Spaces, Matrices, Matrix inverse, Metric Spaces, Norms, Normed Spaces, Inner Products, Inner Product Spaces, Completeness). -
5 - Linear system representations: Frequency domain, transfer functions and state space. Transformations between frequency domain and state space -
6 - Linear Operators: Range and Null Spaces, Eigenvalues, Eigen vectors, Cayley-Hamilton Theorems -
7 - Canonical Forms: Diagonal and Jordan Canonical forms. Various cases. -
8 - Solution of linear dynamical systems equations. State Transition Matrix concept. -
9 - Methods of derivation and computation of state transition matrices -
10 - MID-TERM EXAM -
11 - Connections to nonlinear systems, linearization, equilibrium concepts. -
12 - Stability: Stability definitions, local stability, global stability, asymptotic stability, stability in the sense of Lyapunov, stability analysis of systems in frequency domain or state space. -
13 - Controllability and Observability -
14 - Controllable and Observable Canonical Forms. Controller and Observer Designs -
15 - Issues associated with Controllability and Observability -
16 - FINAL EXAM -
17 - FINAL EXAM -