Péter Gáspár, Zoltán Szabó, József Bokor

Discrete Feedback Systems 1.

Classical Control


Appendix

Basic notations
F
a field,usually the field of real (R) or complex (C) numbers.
Fk
k-vectors,over F.
Fm×n
m × n matrices over F.
Re(z), Im(z)
real and imaginary part of z  C.
λ(A)
eigenvalue of the matrix A.
ρ(A)
spectral radius of the matrix A.
σ ¯(A)
largest singular value of the matrix A.
σ_(A)
smallest singular value of the matrix A.
Sn
the symmetric n × n matrices over R .
Hn
the Hermitian n × n matrices over C.
Ik
the k × k identity matrix.
MT
transpose of a matrix M.
M*
complex-conjugate transpose of a matrix M.
in(A)
the inertia of a symmetric matrix A.
M
the Moore-Penrose pseudoinverse of a matrix M.
Im(M)
the image of a matrix M.
Ker(M)
the kernel of a matrix M.
M
a matrix whose columns form a basis of Ker(M).
M
M * is an arbitrary basis matrix in Ker(M*).
U
the orthogonal complement of a subspace U.
A>0 or A>0
the symmetric matrix A is positive or negative definite.
A0 or A0
the symmetric matrix A is positive or negative semi-definit.
A>0
A and B are symmetric matrices and AB > 0.
A12
for A > 0 the unique Q = QT Q=QT such that Q > 0 and Q2 = A.
Tr(A)
the trace of a symmetric matrix A.
det(A)
the determinant of a symmetric matrix A.
λ(A)
the set of all eigenvalues of a square matrix A.
M
the spectral or .2 norm of a vector or matrix M.
x,y=xTy
the standard scalar product of the vectors v F n.
L(U,V)
the vector space of the U  V linear maps.)

Discrete Feedback Systems 1.

Tartalomjegyzék


Kiadó: Akadémiai Kiadó

Online megjelenés éve: 2019

ISBN: 978 963 454 372 5

The aim of the book is to provide a well-rounded exposure to analysis, control and simulation of discrete-time systems. Theoretical techniques for studying discrete-time linear systems with particular emphasis on the properties and design of sampled data feedback control systems are introduced. This book is intended to be used as a textbook in our MSc and PhD courses. We have tried to balance the broadness and the depth of the material covered in the book. The interested reader is also sent to consult the publications of the references list.

Hivatkozás: https://mersz.hu/gaspar-szabo-bokor-discrete-feedback-systems-1//

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