книги / Матричное исчисление с приложениями в теории динамических систем

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18.6. Stability of non-autonomous systems............................................			384
18.6.1. A linear homogeneous system (384). 18.6.2. Stability of
quasi-linear systems (390). 18.6.3. On stability of a non-linear
process by the first approximation (392).
Chapter 19. АГ^-stabiIity at a finite time interval and technical stability.....			396
19.1. Л ^ -stability at a finite time interval.............................................			396
19.2. K ®-stability and technical stability..............................................			398
S e c t i o n I V	T h e c o n t r o l t h e o r y
Chapter 20. The controlled systems...............................................................			400
20.1. The concept of controlled systems..................................................			400
20.2. The task of control.........................................................................			403
20.3. Two ways to solve the task of control.............................................			405
20.4. The main tasks of the control theory..............................................			408
20.4.1. Linear controlled systems (409). 20.4.2. Linearisation of
non-linear systems (410).
Chapter 21. Controllability of linear systems.................................................			412
21.1. The concept of controllability........................................................			412
21.2. Transformation of a system to a form suitable for studying.............			413
21.3. Necessary and sufficient conditions for controllability.....................			415
21.4. Construction of law of control with feedback for an absolutely
controlled system..............................................................................			420
21.5. Representation of the controllability criterion via the matrix of
controllability...................................................................................			421
21.6. The criterion of controllability for linear stationary systems...........			424
21.7. The structure of the space of states ofa		linear controlled system....	426
21.8. The structure of the space of states of a		stationary system..............	429
21.9. Controllability' of a system, determined by a single high-order
differential equation..........................................................................			432
21.10. Reduction of a totally controlled stationary system with the
scalar control to a single high-order equation.....................................			434
21.11. The capability' of stabilisation of linear stationary systems............			437
21.12. Zero-controllability of linear systems............................................			439
21.13. Autonomy of linear systems..........................................................			441
Chapter 22. Observability of linear systems...................................................			443
22.1. The concept of observability...........................................................			443
22.2. The necessary and sufficient conditions for observability................			444

22.2.1.Invariance of observability properties (444).

22.3.The principle of duality in the theoryof controllability and

observability......................................................................................	447
22.4. The criterion of observability in terms of the observability matrix....	449

22.5. Separation of a not totally observable subsystem from a linear

system..................................................................................................................		451
22.6. The asymptotic identifier............................................................................		453
Chapter 23. The dynamic characteristics of linear system s................................		457
23.1. The unit step-function and the delta-function.........................................		457
23.2. Reaction of the system to an input signal in the form of delta-
function. The impulse transition function....................................................		459
23.3. Connection between input and output signals via the impulse
transition function.............................................................................................		461
23.4. Reactions of the system to an input signal in the form of the
derivative and the integral of the delta-function........................................		463
23.5. Transformation of initial conditions at the system output into an
equivalent input signal....................................................................................		464
23.6. Determination of a differential equation by the impulse function		465
23.7. Construction of the impulse transition function.....................................		467
23.7.1. A stationary system (467). 23.7.2. A non-stationary system
(467).
Chapter 24. Approximate integration of a controlled process equations........		472
24.1. The integro-differential system of equations of a controlled
process................................................................................................................		472
24.1.1. On existence and structure of transformation to		a
differential system (473). 24.1.2. On method of construction of the
approximate solution of the equations (475).
24.2. Reduction of the controlled process equations to a decomposed
differential system (the method of successive approxim ations)..............		475
24.3. The approximate integration of equations of a controlled process
given a small impact of the regulator upon the process (case A )...........		479
24.3.1. Construction of the formal solution	(480). 24.3.2. The
approximate solution of the system (483).
24.4. The approximate integration of equations of a controlled process
(case B)...............................................................................................................		484
24.4.1. Construction of the formal solution	(484). 24.4.2. The
approximate solution of the system (487).
Chapter 25. Some canonical forms of linear process equations..........................		489
25.1. Transformation of a system of equations with constant
coefficients to the decomposed form .............................................................		489
25.1.1. A homogeneous system (489). 25.1.2. A non-homogeneous
system (491).
25.2. Formal transformations of a non-stationary	system ............................	491
25.2.1. A homogeneous system (493). 25.2.2. The case of simple
eigenvalues (496). 25.2.3. A non-homogeneous system (496).
25.3. Equations of a controlled process in the canonical form .....................		499

Chapter 26.	The asymptotic decomposition ofequations of
a multi-dimensional non-stationary linear system by
selecting a structure of the control matrix.........................................			501
26.1. The task formulation................................................................			501
26.2. The algorithm of formal decomposition of the equation (26.1.6)			502
26.3. Study of the equation (26.2.8)			504
26.4. Determination of A'***,		and Bk	510
26.4.1. Construction of		and A[A1 having A, //and BQpre
assigned (511). 26.4.2. Construction of Bk (512). 26.4.3. Con
struction ofthe pseudo-reciprocal matrix F+(514).
26.5. The approximate solution ofthe equation (26.1.6).......................			515
Chapter 27.	Synthesis of linear controls of a multi-dimensional
non-stationary linear system with a diagonal matrix.............................			516
27.1. The task formulation.................................................................			516
27.2. On diagonalisation of a system of equations ofa controlled
process......................................................................................			517
27.3. The method of asymptotic transformation ofequations of
a controlled process to a system of equations with a matrix close
to diagonal one..............................................................................			520
27.3.1. Construction of matrices K„t X„ (522). 27.3.2. Determi-
nation of Kyc \ Xlc*having # 0 and i^pre-assigned (523).
References	................................................................................................		527

Абгарян Карлен Арамович

МАТРИЧНОЕ ИСЧИСЛЕНИЕ С ПРИЛОЖЕНИЯМИ В ТЕОРИИ ДИНАМИЧЕСКИХ СИСТЕМ

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