AE 695 State Space Methods
Contents
  1. Linearization of nonlinear systems
  2. Linear algebra (Ref. 3, 5, 6)
    1. Fields and vector spaces
    2. Subspaces
    3. Linear dependence, dimension, span, basis
    4. Linear operators, kernel, range
    5. Matrix representation of operators, change of bases,
  3. Matrix theory (Refs. 2, 3, 4)
    1. Range and rank of a matrix
    2. Orthogonal complement, kernel and nullity of a matrix
    3. Systems of linear algebraic equations
    4. Eigenvalues, diagonalization, Jordan canonical form
    5. Symmetric matrices and quadratic functions, Sylvester's criterion (Ref. 1, 2)
  4. Linear systems
    1. Matrix exponential and its properties (Ref. 1, 2, 3, 4, 5)
    2. Modal analysis and stability (Ref. 1, 2, 3, 4, 5)
    3. Lyapunov equation (Ref. 1, 2, 3, 4, 5)
    4. Controllability (Ref. 1, 2, 3, 5)
    5. Observability (Ref. 1, 2, 3, 5)
    6. Kalman decomposition theorem
    7. Transfer matrices, poles
    8. Realizations
    9. State feedback, stabilizability
    10. Observers, detectability

Main references

  1. T. Kailath, Linear Systems, 1980. (Kept in study room section.)

Other references
  1. W. J. Rugh, Linear systems theory, 1996.
  2. P. E. Sarachik, Principles of linear systems, 1997.
  3. J. D. Aplevich, Essentials of linear state-space systems, 2000.
  4. R. J. Schwarz, B. Friedland, Linear Systems, 1965.
  5. C. A. Desoer, Notes for a second course on linear systems, 1970.
  6. L. Zadeh, C. A. Desoer, Linear systems theory: The state-space approach, 1963.(see appendix)
  7. B. Friedland, Control system design: A state space approach, 1986.