ECE 60200 - Lumped System Theory

Course Details

Lecture Hours: 3 Credits: 3

Areas of Specialization:

  • Automatic Control

Counts as:

Normally Offered:

Each Fall, Spring, Summer

Requisites by Topic:

It is expected that you are familiar with the Laplace transform and ordinary differential equations. Knowledge of undergraduate feedback control is not strictly needed for most topics, but will definitely increase your appreciation of some of the topics covered in this course. Knowledge of linear algebra is needed. Although officially MATH 511 is listed as a co-prerequisite of this course, in practice, students who took MATH 511 and this course in the same semester often found it challenging as the pace of the two courses may not be fully synchronized.

Catalog Description:

An investigation of the basic theory and techniques of modern system theory, emphasizing linear state model formulations of continuous and discrete time systems in the time domain and frequency domain. Coverage includes notions of linearity, time invariance, discrete and continuous times state models, canonical forms, associated transfer functions and impulse response models, the state transition matrix, the Jordan form, controllability, observability, and stability.

Required Text(s):


Recommended Text(s):

  1. A Linear Systems Primer , Antsaklis, P. J.; Michel, A. N. , Birkhauser Boston , 2007 , ISBN No. 0817644601
  2. Linear System Theory , 2nd Edition , Rugh, W. J. , Pearson , 1995 , ISBN No. 0134412052
  3. Linear System Theory and Design , 4th Edition , C. T. Chen , Oxford Press , 2013 , ISBN No. 978-0199959570
  4. Linear Systems , Kailath, T. , Prentice Hall , 1980 , ISBN No. 0135369614
  5. Systems & Control , Zak, S. H. , Oxford University Press , 2003 , ISBN No. 0195150112

Learning Outcomes

A student who successfully fulfills the course requirements will have demonstrated an ability to:

  • Construct models for dynamical systems arising in various applications, such as: mechanical, electrical, pneumatic, hydraulic, economic, and biological systems
  • Recognize various properties of given linear systems, such as: stability, controllability, observability, stabilizability, and detectability
  • Design controllers so that a system satisfies given performance specifications
  • Test and validate the controller design using simulation tools, such as MATLAB and Simulink

Lecture Outline:

Lectures Topic
3 Basic Concepts, Vocabulary, and Notation of Systems and State Models
2 Formal Definition and Examples of Linear Time Invariant and Time Varying State Models for Lumped Systems
4 Canonical State Models from Ordinary Differential Equations
2 Newton Raphson Technique and Numerical Simulation of State Models
2 Linear Discrete Time State Models: Basics and Parallel w/Continuous Time Case
2 Existence and Uniqueness of Solutions
4 State Transition and Fundamental Matrices of Linear Time Varying State Model
2 Closed Form Solution to Linear Time Varying State Model
3 Eigenvalue-Eigenvector Techniques for Computing e At
3 Discrete Time State Models
4 Impulse Response Matrices and Transfer Function Matrices
4 Controllability of Linear Time Invariant State Models
3 Observability of Linear Time Invariant State Models
4 BIBS and BIBO Stability
3 Exams

Assessment Method:

Homework, exams. (3/2022)