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Ingegneria Informatica/Computer engineering (Academic Year 2009/2010)

Introduction to System theory


Credits: 5
Content language:English
Course description
The aim of the course is to provide an introduction to system theory for dynamical systems. Knowledge of linear algebra, differential equations and physics is recommended.
Prerequisites
Mathematic Analysis II, Physics II
Objectives
A fundamental requirement in several Engineering areas is to be able of representing and interpreting phenomena and complex objects. Through the use of the oriented dynamical system paradigm, System Theory provides a methodological set for dealing with systems classified on the bases of their mathematical description. The aim of the course is to provide the students an introduction to the basic methodologies for the study of dynamical systems and in particular to the class of linear time-invariant systems (continuous time and discrete time).
Program
  • Dynamical System and their state Representation
  • Linear, Time-invariant Differential/ Difference Representations
  • Analysis in the time domain
  • Analysis in the complex variable domain
  • Study of the frequency behavior
  • Transfer function and Realization problems
  • An introduction to stability theory
  • The internal structure properties
  • Interconnected systems: model computation
Book
to be defined
Exercises
The proposed exercises are each related to the macro-areas in which the course is partitionned. The exercises have the following objectives
- To Evaluate the level of knowledge acquired in the field
- To stimulate a discussion for a deeper comprehension of the subject
- To introduce new concepts which are at the bases of the analysis of dynamical systems.

The evaluation takes into account these aspects
Professor
Professor not available
List of lessons
    •  Lesson n. 1: Definition of Dynamical System
    •  Lesson n. 2: The Class of Systems under study
    •  Lesson n. 3: An introduction to the methodologies
    •  Lesson n. 4: Approximate representations
    •  Lesson n. 5: Linear representations: Analysis in the time domain
    •  Lesson n. 6: The transition matrix
    •  Lesson n. 7: Free modes for continuous time systems
    •  Lesson n. 8: Discrete time systems: time domain analysis
    •  Lesson n. 9: The Laplace Transform in the study of continuous time systems
    •  Lesson n. 10: The steady state response and the frequency behavior
    •  Lesson n. 11: Analysis in the complex domain for continuous time systems
    •  Lesson n. 12: Bode Diagrams
    •  Lesson n. 13: The Zeta transform in the study of discrete time systems
    •  Lesson n. 14: Analysis in the complex domain for discrete time systems
    •  Lesson n. 15: Analysis in the complex domain: the general case
    •  Lesson n. 16: From the input-output model to the state representation
    •  Lesson n. 17: Further issues on the state representation
    •  Lesson n. 18: Stability: definitions and conditions
    •  Lesson n. 19: Internal Stability for linear systems
    •  Lesson n. 20: Lyapunov methods for the stability analysis
    •  Lesson n. 21: Structural properties: reachability and observability
    •  Lesson n. 22: Kalman decomposition
    •  Lesson n. 23: Interconnected systems: elementary connections and their properties
    •  Lesson n. 24: Interconnected systems: on the computation of the associated transfer function and state representation
    •  Lesson n. 25: A synthesis