© National Instruments Corporation 2-1 Xmath Control Design Module
2
Linear System Representation
Xmath provides a structure for system representation called a system
object. This object includes system parameters in a data structure designed
to reflect the way these systems are analyzed mathematically. Operations
on these systems are likewise defined using operators that mirror as closely
as possible the notation control engineers use. This chapter outlines the
types of linear systems the system object represents and then discusses the
implementation of a system within Xmath. The functions used to create a
system object and to extract data from this object are an intrinsic part of the
object and are also described. Finally, this chapter discusses the functions
check( ), discretize( ), and makecontinuous( ), which use
information stored in the system object to convert systems from one
representation to another.

Linear Systems Represented in Xmath

Xmath handles finite-dimensional, linear, and time-invariant linear
systems in both discrete and continuous time. These systems take one
of the forms shown in Table 2-1.
The transfer function representation can be used to describe single-input,
single output (SISO) systems only; there are no restrictions on the number
of input and outputs that can be specified for a state-space system. All of
these systems can be created using the Xmath system( ) function.
Table 2-1. Summary of Linear Systems
System Type Continuous Time Discrete Time
State-spec
Transfer function
x
·Ax Bu+=
yCxDu+=
xk1+AxkBuk
+=
ykCxkDuk
+=
Hs() CsI A–()
1–BD+= Hz() CzI A–()
1–BD+=