Péter Gáspár, Zoltán Szabó, József Bokor

Discrete Feedback Systems 2.

Modern Control


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 2.

Tartalomjegyzék


Kiadó: Akadémiai Kiadó

Online megjelenés éve: 2019

ISBN: 978 963 454 373 2

The classical control theory and methods that we have been presented in the first volume are based on a simple input-output description of the plant, expressed as a transfer function, limiting the design to single-input single-output systems and allowing only limited control of the closed-loop behaviour when feedback control is used. Typically, the need to use modern linear control arises when working with models which are complex, multiple input multiple output, or when optimization of performance is a concern. Modern control theory revolves around the so-called state-space description. The state variable representation of dynamic systems is the basis of different and very direct approaches applicable to the analysis and design of a wide range of practical control problems. To complete the design workflow, finally some introduction into system identification theory is given.

Hivatkozás: https://mersz.hu/gaspar-szabo-bokor-discrete-feedback-systems-2//

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