Neumann M., Berman A., Stern R.J. — Nonnegative matrices in dynamic systems :: Электронная библиотека попечительского совета мехмата МГУ

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Neumann M., Berman A., Stern R.J. — Nonnegative matrices in dynamic systems

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Название: Nonnegative matrices in dynamic systems

Авторы: Neumann M., Berman A., Stern R.J.

Аннотация:

This work applies the theory of nonnegative matrices to problems arising in positive differential and control systems. There is a concise review of requisite material in convex analysis and matrix theory, as well as a detailed review of linear differential and control systems. Exposition incorporates simple real-world dynamic models to better illustrate various aspects of the theory being developed. Contains exercises.

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Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1989

Количество страниц: 192

Добавлена в каталог: 23.05.2011

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Предметный указатель

$\mathscr{K}$ -irreducible matrix      17
$\mathscr{K}$ -monotone matrix      20
$\mathscr{K}$ -monotone on a set matrix      22
$\mathscr{K}$ -nonnegative matrix      16
$\mathscr{K}$ -positive matrix      16
$\mathscr{K}$ -semipositive matrix      21
$\mathscr{K}$ -semipositive on $\mathscr{L}_{A}$ , matrix      21
(A, B)-invariance      67
Accessability      25
Admissible control      36
Affine hull      2
Affine set      2
Almost exponentially $\mathscr{K}$ -irreducible matrix      71
Almost monotone with respect to $\mathscr{K}$ -matrix      24
Attainable point      36
Attainable set      36
avoidance      96
Bang-bang principle      47
Caratheodory's theorem      1
Cauchy — Euler scheme      115
Cayley — Hamilton theorem      10
Chain      25
Companion form      49
Concatenation      32
Cone      4
Cone, dual      5
Cone, pointed      4
Cone, proper      4
Cone, simplicial      100
Cone, solid      4
Conical hull      4
Control restraint set      35
Controllability, complete      37
Controllability, global      37
Controllability, strong      37
Controllable point      36
Controllable set      36
Controllable space      42
Convergent matrix      13
Convex combination      1
Convex hull      1
Convex set      1
Core      111
Definable matrix function      1
Degree      10
Diagonally stable matrix      22
Directed graph      19
Discrete reachability cone      116
Distinguished vertex      25 26
Dominant power      96
Drazin inverse      14
Dual cone      5
Effective part of boundary      110
Eigenspace      10
Essentially $\mathscr{K}$ -irreducible matrix      19
Essentially $\mathscr{K}$ -nonnegative matrix      19
Essentially $\mathscr{K}$ -positive matrix      19
Essentially nonnegative matrix      19
Essentially positive matrix      19
Eventual avoidance      98
Exponential nonnegativity      61
Exponentially $\mathscr{K}$ -irreducible matrix      71
Exponentially $\mathscr{K}$ -nonnegative matrix      71
Exponentially $\mathscr{K}$ -positive matrix      71
Extended M-matrix      85
Extreme point      2
Face      3
Feedback holdability      125
Final vertex      25
Finitely generated set      3
Frobenius normal form      25
Generalized eigenspace      10
Generalized eigenvector      10
Generalized left inverse      14
Geometric multiplicity      10
Group inverse      14
Group invertible M-matrix      23
Halfspace      3
Hausdorff distance      6
Hit and hold problem      125
Holdability      64
Holdability feedback      125
Hull, affine      2
Hull, conical      4
Hyperplane      2
Hyperplane, separating      3
Hyperplane, strictly separating      3
Hyperplane, supporting      3
INDEX      13
Initial vertex      25
Input-output relation      52
Jordan block      9

Jordan canonical form      10
Jordan chain      11
Linear control system      35
Linear equivalence      49
Linear feedback law      50 125
Linear observed process      50
M-matrix      20
M-matrix with respect to $\mathscr{K}$       20
M-matrix, extended      85
M-matrix, group invertible      23
Matrix, $\mathscr{K}$ -irreducible      17
Matrix, $\mathscr{K}$ -monotone      20
Matrix, $\mathscr{K}$ -monotone on a set      22
Matrix, $\mathscr{K}$ -nonnegative      16
Matrix, $\mathscr{K}$ -positive      16
Matrix, $\mathscr{K}$ -semipositive      21
Matrix, $\mathscr{K}$ -semipositive on $\mathscr{L}_{A}$       21
Matrix, almost exponentially $\mathscr{K}$ -irreducible      71
Matrix, almost monotone with respect to $\mathscr{K}$       24
Matrix, convergent      13
Matrix, diagonally stable      22
Matrix, essentially $\mathscr{K}$ -irreducible      19
Matrix, essentially $\mathscr{K}$ -nonnegative      19
Matrix, essentially $\mathscr{K}$ -positive      19
Matrix, essentially nonnegative      19
Matrix, essentially positive      19
Matrix, exponentially $\mathscr{K}$ -irreducible      71
Matrix, exponentially $\mathscr{K}$ -nonnegative      71
Matrix, exponentially $\mathscr{K}$ -positive      71
Matrix, nonnegative      18
Matrix, positive      18
Matrix, semiconvergent      13
Matrix, stochastic      27
McMillan degree      52 156
Minimal realization      52 156
Nearly periodic      35
Nonnegative matrix      18
Nonsingular vertex      26
Normal vector      3 4
Normality      154
Observability      50 147
Observation set      50 146
Outward normal vector      3
Periodic solution      35
PF vertex      25
Pointed cone      4
Polyhedral set      3
Positive control system      137
Positive invariance      61
Positive matrix      18
Positive realization      156—159
Preferred basis      28
Proper cone      4
Proper rational function      52
Reachability cone      93
Real $\lambda$ -block      14
Real canonical form      15
Real generalized eigenspace      15
Realization      52
Reduced graph      25
Rest-control      48
Rest-point      48
Rest-state      48
Semiconvergent matrix      13
Simplicial cone      100
Singular vertex      26
Solid cone      4
Spectral abscissa      19
Spectral radius      13
Stabilizability-holdability      125
Stabilizable      50
Stochastic matrix      27
Strong component      24
Strongly connected      19
Subtangential      65
Subtangential, strictly      65
Subtangential, strongly      71
Terminator      96
Trajectory equivalent      129
Transfer function      52—53 159
Variation of parameters formula      36
Vertex      19 25
Vertex, distinguished      25 26
Vertex, final      25
Vertex, initial      25
Vertex, nonsingular      26
Vertex, PF      25
Vertex, singular      26
Weak compactness      7
Weak convergence      7
Weak limit      7
Z-matrix      19

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