The Stability and Control of Discrete Processes

Abstract

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.