Basics of control theory (issue 3)

1              Introduction
1.1.          Basic concepts and the essence of the automatic control system
1.2.          Classification of automatic control systems
l .3.          Outline of the content of the book and how to use it
1.4.          Description of linear dynamic systems
1.5.          Static and dynamic systems, fixed and non-stationary
1.5.1.       Behavioristic definition of the system
1.5.2.       Relational definition of the system
1.6.          Linearization of non-linear systems
1.6.1.       The method of developing into a series
1.6.2.       The optimal linearization method
1.6.3.       Non-linear feedback method
1.7.          Models of dynamic systems
1.7.1.       Electrical systems
1.7.2.       Mechanical systems
1.7.3.       Electromechanical systems
1.7.4.       Mixing processes
1.7.5.       Systems with distributed parameters
1.7.6.       Logistic equation in biology
1.7.7.       Lotki-Yolterry model of the victim predator system

1.7.8.       Model Maya predator system - victim
1.7.9.       Sol model of economic growth
1.7.10.    The Leontief model produced in interior sectors
Works
2.             Mathematical models of linear continuous and discrete dynamic systems
2.1.          Introduction
2.2.          Time models
2.2.1.       Differential and differential equations
2.2.2.       State variables
2.2.3.       Model of continuous state variables
2.2.4.       Model of discrete state variables
2.2.5.       The equation of the output of the state variable model
2.2.6.       AR / ARMA and ARMAX models
2.2.7.       Incremental characteristics and pulse characteristics
2.2.8.       How to do it in MATLAB
2.3.          Frequency models
2.3.1.       Operator transmittance
2.3.2.       Spectral transmission
2.3.3.       How to do it in MATLAB
2.4.          Basic dynamic units
2.4.1.       A zero-failure unit
2.4.2.       The integral integral element
2.4.3.       Differentiating member ideal
2.4.4.       First order inertial member
2.4.5.       Delaying member
2.4.6.       The integral integrating member
2.4.7.       Differentiating real element
2.4.8.       Second order inertial member
2.4.9.       Oscillating member
2.4.10.    Works
2.5.          The relationship between the state variable model and the input-output model
2.5.1.       Mutual relations between models
2.5.2.       How to do it in MATLAB
2.6.          Works
3.             Mathematical models of non-linear dynamical systems
3.1.          Introduction
3.2.          Phase plane analysis
3.2.1.       Concepts of phase plane analysis
3.2.2.       Creating a phase portrait
3.2.3.       Analysis of linear systems by phase plane method
3.2.4.       Analysis of non-linear systems using the phase plane method
3.2.5.       Summary
3.2.6.       How to do it in MATLAB
4.             Properties of systems
4.1.          Stability of dynamic systems
4.1.1.       Concepts related to stability
4.1.2.       Stability testing of linear continuous systems
4.1.3.       Criteria for stability of continuous systems
4.1.4.       Study of the stability of linear discrete systems
4.1.5.       Lapun's theory of stability of non-linear systems
4.1.6.       Methods for the selection of the Lapunov function
4.1.7.       Summary
4.1.8.       How to do it in MATLAB

4.2.          The feasibility, controllability, observability and reproducibility of linear systems
4.2.1.       The availability of discrete systems
4.2.2.       Controllability to zero and controllability of discrete systems
4.2.3.       Observability of discrete systems
4.2.4.       Reproducibility of discrete systems
4.2.5.       Discrete dual systems
4.2.6.       Initial availability of discrete systems
4.2.7.       Achievability and controllability of continuous systems
4.2.8.       Observability and reproducibility of continuous systems
4.2.9.       Stabilization and detection of discrete and continuous systems
4.2.10.    Steam decomposition (A, B) and (A, C)
4.2.11.    Kalman decomposition of linear systems
4.2.12.    A set of reachable states and .R-controllability of singular circuits
4.2.13.    Controllability and pulse control of singular circuits
4.2.14.    R-observability of singular circuits
4.2.15.    The observability of singular circuits
4.2.16.    Pulse observability of singular circuits
4.2.17.    Decomposition of singular circuits
4.2.18.    How to do it in MATLAB
4.3.          Zero and Poles
4.3.1.       SISO systems
4.3.2.       Smith's form of the matrix
4.3.3.       Multidimensional MIMO systems
4.3.4.       Poles and zeros in infinity
4.4.          Canonical characters
4.4.1.       Reduction of the matrix to the form of Frobenius
4.4.2.       Reduction of the matrix to Jordan's canonical form
4.4.3.       The canonical forms of a matrix of systems with one input
4.4.4.       The canonical forms of a matrix of systems with one output
4.4.5.       The canonical forms of a matrix of systems with many inputs
4.4.6.       The canonical forms of a matrix of systems with many outputs
4.4.7.       The canonical forms of the matrix of singular circuits
4.4.8.       How to do it in MATLAB
4.5.          Works
AND.             Basics of matrix calculus
Al           Basic types of matrices
A.2.         The determinant of the matrix and its properties
A.3.         Basic operations on matrices
A.4.         Minors and determinant of matrix product and row of matrices
A.5.         Nucleus and image of the matrix
A.6.         Left and right inverse of the matrix
A.7.         Solving a system of linear equations
A.8.         Eigenvectors and eigenvectors of the matrix
A.9.         Distribution of matrices against eigenvalues and specific values
A. 10.      Square forms positively defined
A.11.       Standards of vectors and matrices
A. 12.      Moore-Penrose pseudo-reverse matrix
A. 13.      The polynomial null and minimal matrix and the Sylvester pattern
A.14.       Block matrices
A. 15.      Kronecker product of the matrix
A.16.       How to do it in MATLAB
B.             Differential and differential equations
bl           Diversification and integration of the matrix
B.2.         Differential equations
B.3.         Differential equations
B.4.         Matrix Riccatie's differential equation
B.5.         The Lie derivative of the scalar function along the field vector

B.6.         Parenthesis of Lie fields vector
B.7.         Distributions, involute distributions and invaluable distributions
B.7.1.      distributions
B.7.2.      Involutive distributions
B.7.3.      Imperative distributions
C.             Integral transformations
cl           Laplace transformation and its properties

C.1.1.      Laplace transformation

C.1.2.      Basic properties of Laplace transform
C.1.3.      Inverse Laplace transformation and determination of the original of a given transform
C.1.4.      Solving differential equations using the operator method
D.2.         Transforming Z and its properties
C.2.1.      Transformation Z
C.2.2.      Basic properties of transformation Z
C.2.3.      Reverse Z transformation and determination of the original of the given transform
C.2.4.      Solving differential equations using the operator method
C.2.5.      How to do it in MATLAB
Bibliography
Index