Notation 
Meaning 

Continuoustime variable 

Continuoustime signal 

Discretetime variable 

Discretetime 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 impulsesampled version of 

Fourier
transform of ... 

Laplace transform of ... 

Deltatransform of ... 

Ztransform of
... 

inverse Fourier transform of ... 

inverse Laplace transform of ... 

inverse Deltatransform of ... 

inverse
Ztransform of ... 

Laplacetransform complex variable 

angular frequency 

Deltatransform complex
variable 

Ztransform complex variable 

Fourier
transform of 

Laplace transform of 

Deltatransform of 

Ztransform 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 squareintegrable
along the imaginary axis and analytic in the righthalf plane 

Hilbert space of those functions absolutely
integrable along the imaginary axis 

Hilbert space
of those functions squareintegrable along the imaginary axis. 

Hilbert space of those functions bounded along
the imaginary axis and analytic in the righthalf plane 

Hilbert space of those rational
functions bounded along the imaginary axis and analytic in the
righthalf 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 zeroorder hold 

transfer function of a firstorder hold 

operator notation, i.e.
operates on ... 

composite operators, i.e.,


identity matrix in

d.c. 
direct current, i.e.,
zerofrequency signal 
d.o.f. 
degrees of freedom 
CTARE 
ContinuousTime Algebraic Riccati Equation 
DTARE 
DiscreteTime
Algebraic Riccati Equation 
CTDRE 
ContinuousTime Dynamic
Riccati Equation 
DTDRE 
DiscreteTime Dynamic Riccati Equation 
IMC 
Internal Model Control 
IMP 
Internal Model Principle 
LHP 
left halfplane 
OLHP 
open left halfplane 
RHP 
right half
plane 
ORHP 
open righthalf plane 
NMP 
nonminimum phase 
MFD 
Matrix fraction description 
LMFD 
Left matrix fraction
description 
RMFD 
Right matrix fraction description 
LTI 
Linear time invariant 
LQR 
Linear quadratic regulator 
w.r.t 
with respect to ... 

