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Last updated:

August 5, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course provides an introduction to nonlinear deterministic dynamical systems.

Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov’s first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Course Curriculum

  • Input/Output and State-Space Models Unlimited
  • Differential Equations as System Models Unlimited
  • Continuous Dependence on Parameters Unlimited
  • Analysis Based on Continuity Unlimited
  • Lyapunov Functions and Storage Functions Unlimited
  • Storage Functions and Stability Analysis Unlimited
  • Finding Lyapunov Functions Unlimited
  • Local Behavior at Equilibria Unlimited
  • Local Behavior Near Trajectories Unlimited
  • Singular Perturbations and Averaging Unlimited
  • Local Controllability Unlimited
  • Feedback Linearization Unlimited

About the instructor

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Massachusetts Institute of Technology