ECE 5754 Applied Linear Systems | ECE | Virginia Tech


Course Information


Develop an applied understanding of state-space representations for linear time invariant multi-input multi-output dynamic systems in both the time domain and the frequency domain. Introduction to modern state-space control methods: state feedback and output feedback. Realistic design problems with numerical simulations of practical implementations.

Why take this course?

This course provides a hands-on understanding of linear systems with multiple inputs and multiple outputs with an introduction to modern state-space control. The course emphasizes the use of practical software tools for anlayzing stability, computing time responses and frequency responses, and also for designing state feedback and output feedback controllers.


ECE 4405 or ECE 4624 or ECE 4634 or ME 4504 or AOE 4004.

The course requires a background in classical single-input simgle-output control which is not taught until the senior year. The course also requires a strong familiarity with Matlab/Simulink that is uncommon for undergraduates, but is expected of graduate students in the systems and controls disciplines.

Major Measurable Learning Objectives

  • Represent a system of ordinary differential equations as a state-space realization
  • Analyze the stability of a linear time-invariant system
  • Compute the time response and frequency response of a linear time-invariant state-space system
  • Analyze controllability and observability of a linear time-invariant system
  • Design state feedback and output feedback controllers

Course Topics


Percentage of Course

1. Linear algebra and matrix theory 15%
2. State-space representation of systems 10%
3. Transition matrix properties 10%
4. Stability (including internal and input-output) 20%
5. Controllability and observability 10%
6. Minimal realizations 5%
7. Controller and observer forms 5%
8. Linear feedback and state observation 15%
9. Separation principle and duality 5%
10. Integral control and exogenous inputs 5%