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Last updated:

November 8, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

The course addresses dynamic systems, i.e., systems that evolve with time.

Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.

We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.

Course Curriculum

  • Introduction, linear algebra review Unlimited
  • Least square estimation Unlimited
  • Least square solutions of linear problems Unlimited
  • Singular values Unlimited
  • Matrix perturbations Unlimited
  • Dynamical systems Unlimited
  • State-space models Unlimited
  • Solutions of state-space models Unlimited
  • Transfer functions Unlimited
  • I/O stability Unlimited
  • I/O stability (cont.) Unlimited
  • Bode’s sensitivity integral Unlimited
  • Robust stability Unlimited
  • Reachability and observability Unlimited
  • Minimal realizations Unlimited
  • Balanced realization Unlimited
  • Feedback stabilization Unlimited
  • H2 optimization Unlimited
  • H∞ optimization Unlimited

About the instructor

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Massachusetts Institute of Technology