Linear system theory

EE-611

Welcome to the course on Linear Systems TheoryThe ...

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Description

Welcome to the course on Linear Systems Theory

The course is organized as classical lectures covering the following topics divided into

  1. Algebra (Groups, Rings, Fields, Vector Spaces, Modules, Ideals, Quotients)
  2. Linear Systems (Polynomial matrix description, System Matrix, State-Space, Operator Forms)
  3. Invariant Factors (Elementary transforms, Minimal Polynomials, Cyclic Vectors, Smith-MacMillan Form, Input-Output Decoupling Zeros)
  4. Solutions, Matrix Exponential, Stability (Grammians, State-Space Solutions, Differential Algebraic Definition of a System, Lyapunov Functions)
  5. Controllability and Observability (Criteria, Grammians, Ranks, Canonical Forms)
  6. Realization Theory (Markov Parameters, Hankel Matrices, Balanced Realizations)
  7. Regulator Theory (Synthesis of a Controller from the invariant Factors, Multivariable RST)

This will cover the semester. A follow up (in preperation, and could be self-study of one paper for the grading, more on this during the lectures) is the second part.

PART II (Towards Nonlinear Systems)

  1. Motion on Lie Groups and the Lie Algebra (Spacecraft example)
  2. Nilpotent Lie Algebras (Adjoint mapping and the Exponential Map)
  3. Integrable Mechanical Systems using Lie Algebras (the Todda Lattice)
  4. Controllability and Accessibility (Sussmann Jurdjevic Theorems, Sussmann's results)
  5. Functional Expansion and Nonlinear Realization Theory (Chen-Fliess Functional Expansion and Formal Power Series)