The stability and control of discrete processes

Chapter 1 Introduction

Chapter 2 Liapunov’s Direct Method

Chapter 3 Linear systems x’ = Ax.

Chapter 4 An algorithm for computing A n

Chapter 5 A characterization of stable matrices. Computational criteria

Chapter 6 Liapunov’s characterization of stable matrices. A Liapunov function for x’ = Ax

Chapter 7 Stability by the linear approximation

Chapter 8 The general solution of x’ = Ax. The Jordan Canonical Form.

Chapter 9 Higher order equations. The general solution of ψ(z)y = 0.

Chapter 10 Companion matrices. The equivalence of x’ = Ax and ψ(z)y = 0.

Chapter 11 Another algorithm for computing A n .

Chapter 12 Nonhomogeneous linear systems x’ = Ax + f(n). Variation of parameters and undetermined coefficients.

Chapter 14 Systems of higher order equations P(z)y = 0. The equivalence of polynomial matrices.

Chapter 15 The control of linear systems. Controllability.

Chapter 16 Stabilization by linear feedback. Pole assignment.

Chapter 17 Minimum energy control. Minimum time-energy feedback controls.

Chapter 18 Observability. Observers. State Estimation. Stabilization by dynamic feedback.