Linear Systems
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA04305 
Vaknaam  Linear Systems 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Linear Systems  
Leerdoelen  At the end of the course, the student is able to: 1. give examples of physical systems that can be modeled as linear systems, distinguish the roles of inputs, outputs, and state variables in such models, and explain the concept of feedback in improving dynamic properties of a given system. 2. explain the solution structure of linear differential equations. In particular, the student can solve autonomous linear systems using the matrix exponential and Jordan canonical form and can reproduce the general solution of nonautonomous linear systems. 3. explain fundamental concepts of mathematical systems theory such as controllability, observability, stabilizability, and detectability, formulate methods to test these properties and reproduce their proofs. 4. formulate the basic control problems of pole placement, stabilization, and state observation, and reproduce necessary and sufficient conditions for solving these problems. 5. explain the relationship between linear systems and transfer functions using the Laplace transform. In particular, the student can relate transfer function poles to system eigenvalues using the concepts of controllability and observability. 6. apply the theory of the course to design stabilizing controllers using either state or output measurements for examples of simple physical systems. 

Omschrijving  Mathematical systems theory deals with the analysis of models of physical/engineering systems and aims to improve the behavior of such systems by designing feedback controllers. In this introductory course, these models are taken to be linear systems, i.e., sets of coupled linear ordinary differential equations. In particular, finitedimensional systems with inputs and outputs are considered. The course deals with solutions of linear systems (existence and uniqueness, the superposition principle, the matrix exponential) as well as basic concepts and methods in mathematical systems theory: these include linearization, controllability and observability, stability, and transfer functions. Using these concepts, basic control problems will be discussed, namely pole placement, state observation, and stabilization with both state feedback and dynamic output feedback. All concepts will be illustrated with examples from physical/engineering systems. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(The final grade F is computed from the written exam WE and three homework assignments HW1, HW2, HW3 as follows: F = (HW1 + HW2 + HW3)/6 + WE/2. The results of the homework assignments will remain valid for the resit exam.) 

Vaksoort  propedeuse  
Coördinator  dr. ir. B. Besselink  
Docent(en)  dr. ir. B. Besselink  
Verplichte literatuur 


Entreevoorwaarden  The course assumes prior knowledge in linear algebra (as offered in the courses Linear Algebra 1 and 2).  
Opmerkingen  The course prepares for further courses on differential equations as well as courses on systems theory such as "Project Systems Theory", "Advanced Systems Theory", and "Calculus of Variations and Optimal Control".  
Opgenomen in 
