1. Introduction.- 2. Liapunov's direct method.- 3. Linear systems x' = Ax..- 4. An algorithm for computing An..- 5. A characterization of stable matrices. Computational criteria..- 6. Liapunov's characterization of stable matrices. A Liapunov function for x' = Ax..- 7. Stability by the linear approximation..- 8. The general solution of x' = Ax. The Jordan Canonical Form..- 9. Higher order equations. The general solution of ?(z)y = 0..- 10. Companion matrices. The equivalence of x' = Ax and ?(z)y = 0..- 11. Another algorithm for computing An..- 12. Nonhomogeneous linear systems x' = Ax + f(n). Variation of parameters and undetermined coefficients..- 13. Forced oscillations..- 14. Systems of higher order equations P(z)y = 0. The equivalence of polynomial matrices..- 15. The control of linear systems. Controllability..- 16. Stabilization by linear feedback. Pole assignment..- 17. Minimum energy control. Minimal time-energy feedback control..- 18. Observability. Observers. State estimation. Stabilization by dynamic feedback..- References.
