• Linear Dynamical Systems

  
  

  Textbook and optional references

  There is no textbook. Everything we’ll use is posted on the 363 website in pdf format.

  If you’d like to consult some books, we listed some below.

  • LQR and Kalman filtering are covered in many books on linear systems, optimal control, and optimization. One good one is Dynamic Programming and Optimal Control, vol. 1, Bertsekas, Athena Scientific. Another two are Optimal Filtering and Optimal Control: Linear Quadratic Methods, both Anderson & Moore, Dover.
  • Lyapunov theory is covered in many texts on linear systems, e.g., Linear Systems, Antsaklis & Michel, McGraw-Hill.
  • Nonlinear Lyapunov theory is covered in most texts on nonlinear system analysis, e.g., Nonlinear systems: Analysis, Stability, and Control, Sastry, Springer, or Nonlinear Systems Analysis (2nd edition), Vidyasagar, SIAM.
  • Lots of material on LMIs can be found in Boyd, El Ghaoui, Feron, and Balakrishnan, Linear Matrix Inequalities in System and Control Theory, but this is not a book for casual browsing.
  
  
  
  

  Lecture Slides

  Professor Stephen Boyd, Stanford University, Winter Quarter 2008-09
  These lecture slides are still changing, so don’t print them yet.
  1. Linear quadratic regulator: Discrete-time finite horizon
  2. LQR via Lagrange multipliers
  3. Infinite horizon LQR
  4. Continuous-time LQR
  5. Linear quadratic stochastic control
  6. Invariant subspaces
  7. Estimation
  8. The Kalman filter
  9. Approximate nonlinear filtering
  10. Linear quadratic stochastic control with partially observed states
  11. Conservation and dissipation
  12. Basic Lyapunov theory
  13. Linear quadratic Lyapunov theory
  14. Lyapunov theory with inputs and outputs
  15. Linear matrix inequalities and the S-procedure
  16. Analysis of systems with sector nonlinearities
  17. Perron-Frobenius theory
      
      
      
      
      Support Notes
      Professor Stephen Boyd, Stanford University, Winter Quarter 2008-09
      Additional background notes.
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        Riccati recursion derivation
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        Linear quadratic Lyapunov theory notes
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        Solving semidefinite programs using CVX
        
        

        Section Notes

        Professor Stephen Boyd, Stanford University, Winter Quarter 2008-09
        The (optional) problem sections are every second Tuesday, 5:15–6:05 pm, in Hewlett 103.
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          Notes from 1/20/09
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          Notes from 1/27/09
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          Slides from 2/10/09
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          Notes from 2/24/09
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          Slides from 3/10/09