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The stability and control of discrete processes

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Cover of 'The stability and control of discrete processes'

Table of Contents

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