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## A. Notation, Symbols, and Acronyms

Notation Meaning
Continuous-time variable
Continuous-time signal
Discrete-time variable
Discrete-time sequence
Sampling period
Sampled version of
Delta operator
forward shift operator
Kronecker delta
Dirac delta
Expected value of ...
Controllability matrix in state space description
Observability matrix in state space description
Set of eigenvalues of matrix ...
unit step (continuous time) at time
unit step (discrete time) at time
Dirac impulse-sampled version of
Fourier transform of ...
Laplace transform of ...
Delta-transform of ...
Z-transform of ...
inverse Fourier transform of ...
inverse Laplace transform of ...
inverse Delta-transform of ...
inverse Z-transform of ...
Laplace-transform complex variable
angular frequency
Delta-transform complex variable
Z-transform complex variable
Fourier transform of
Laplace transform of
Delta-transform of
Z-transform of
Time convolution of and
Complex convolution of and
real part of ...
imaginary part of ...
set of all matrices with complex entries
Hilbert space of those functions square-integrable along the imaginary axis and analytic in the right-half plane
Hilbert space of those functions absolutely integrable along the imaginary axis
Hilbert space of those functions square-integrable along the imaginary axis.
Hilbert space of those functions bounded along the imaginary axis and analytic in the right-half plane
Hilbert space of those rational functions bounded along the imaginary axis and analytic in the right-half plane
Hilbert space of those functions bounded along the imaginary axis.
set of all natural numbers
set of real numbers larger than zero
set of real numbers smaller than zero
set of all matrices with real entries
set of all real rational functions with (finite) poles strictly inside the LHP
set of all integer numbers
Matrix where the element in the row and column is denoted by
element in the row and of matrix
row of matrix
columm of matrix
complex conjugate of ...
transfer function of a zero-order hold
transfer function of a first-order hold
operator notation, i.e. operates on ...
composite operators, i.e.,
identity matrix in
d.c. direct current, i.e., zero-frequency signal
d.o.f. degrees of freedom
CTARE Continuous-Time Algebraic Riccati Equation
DTARE Discrete-Time Algebraic Riccati Equation
CTDRE Continuous-Time Dynamic Riccati Equation
DTDRE Discrete-Time Dynamic Riccati Equation
IMC Internal Model Control
IMP Internal Model Principle
LHP left half-plane
OLHP open left half-plane
RHP right half- plane
ORHP open right-half plane
NMP nonminimum phase
MFD Matrix fraction description
LMFD Left matrix fraction description
RMFD Right matrix fraction description
LTI Linear time invariant