/EE6415-Assignments

Primary LanguageMATLAB

EE6415-Assignments

Assignments and the endsemester exam given in the course Nonlinear Systems Analysis (EE6415), Spring 2022. Reports' .tex files will be shared on request.

Assignment-1:

  • Phase portraits of nonlinear systems in MATLAB and guessing the nature of stablity through them

Assignment-2:

  • Stability using Linearization
  • Limit cycles existence (Poincare-Benedixson criterion)

Assignment-3:

  • Finding and classifying bifurcations
  • Non-Existence of periodic orbit (Benedixson Theorem)
  • Bifurcation video (evolution of phase portrait)

Assignment-4:

  • Vector and Metric spaces
  • Converging and Cauchy sequences

Assignment-5:

  • Contraction mappings
    • Unique fixed point
  • Lipshitz functions
  • Gronwall-Bellman inequality
  • Comparison Lemma

Assignment-6:

  • Lyapunov stability for linear and nonlinear systems
  • LaSalle's Theorem
  • Lyapunov Candidates: Checking radial unboundedness

Assignment-7:

Control of nonlinear systems using:

  • Feedback linearization:
    • restoring steady state
    • stability
    • finding relative degree
    • checking/showing minimum phase
  • Sliding model control:
    • Boundary layer to remove chattering

Endsem exam:

  • Checking Passivity for Linear systems (Positive Real Lemma) - MATLAB implementation using YALMIP
  • Feedback linearization:
    • reference tracking
    • finding relative degree
    • checking/showing minimum phase
    • zero dynamics
    • output design
  • Passivity based control
  • Sliding model control
  • Stability analysis: Lyapunov stability and La Salle's Principle