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ECE 5744 - Linear Systems Theory (3C)

Course Description

Advanced introduction to the theory of time-varying and time-invariant linear systems represented by state equqtions; solutions of linear systems, uniform stability and other stability criteria, uniform observability and controllability, state feedback and observers.

Why take this course?

This course provides a mathematically rigorous introduction to fundamental concepts in the field of linear systems theory. Concepts are presented in the context of linear time-varying systems, with frequent specialiation to time-invariant systems. This course emphasizes the role of theorems and proofs in mathematical systems theory. The concepts taught in this course are required for advanced studies in modern control theory, but also for signal processing and communication systems.

Learning Objectives

  • Compute the solution of a time-varying linear state equation
  • Prove stability properties of classes of linear time-varying and time-invariant systems
  • Prove controllability and observability properties of time-varying and time-invariant linear state-space systems.
  • Use Kalman decomposition to compute unobservable and/or uncontrollable modes of a time-invariant state-space system
  • State and prove properties of linear time-varying and time-invariant systems under state feedback or observer-based output feedback control