CHAPTER 1 
INTRODUCTION 
The trend of the past few decades has been toward dynamical systems 
that operate with variables which are in the form of a sequence of num- 
bers. These variables are generally quantized in amplitude and are 
available only at specified instants of time, which are usually equally 
spaced. By contrast, a continuous, or analogue, system has variables 
which are continuous functions of time, that is, their values are known 
at all instants of time. Both types of system can have imperfections 
in the amplitude of the signal variables. For instance, the discrete 
system, in which the variables are sequences of numbers, may operate 
with these variables quantized so that even if there is no other source 
of amplitude error, there is the uncertainty in the magnitude equal to one 
quantum. In continuous systems, imperfections in the data-transmis- 
sion and transducing devices, as well as unwanted noise, produce uncer- 
tainties in the amplitude of the system variables which are similar to 
those of the discrete systems. The major point of difference between 
analogue and discrete systems lies in the fact that analogue, or continu- 
ous, systems have variables which are known at all instants of time, 
whereas discrete systems have variables which are known only at sam- 
pling instants. 
A system in which the data appear at one or more points as a sequence 
of numbers or as pulses is known as a sampled-data system. A system in 
which the data are everywhere known or specified at all instants of time 
is known as a continuous, or analogue, system. This book deals with 
sampled-data systems, the theory underlying their operation, and the 
synthesis of systems of this type which fulfill certain practical objectives. 
1.1 The Sampling Operation 
In any dynamical system found in nature, there exist dependent and 
independent variables which are related to each other by linear or non- 
linear differential equations. In the systems approach, independent 
variables are referred to as inputs and dependent variables as outputs. 
In complex systems there are also intermediate variables, which are 
considered as being internal in the system, although they can be brought 
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