Specifications

2-5
Precedence Rules
Operations like addition and commands like feedback operate on more than
one LTI model at a time. If these LTI models are represented as LTI objects of
different types (for example, the first operand is TF and the second operand is
SS), it is not obvious what type (for example, TF or SS) the resulting model
should be. Such typeconflicts are resolved by precedencerules.Specifically,TF,
ZPK, SS, and FRD objects are ranked according to the precedence hierarchy.
Thus ZPK takes precedence over TF, SS takes precedence over both TF and
ZPK, and FRD takes precedence over all three. In other words, any operation
involving two or more LTI models produces:
•An FRD object if at least one operand is an FRD object
•AnSSobjectifnooperandisanFRDobjectandatleastoneoperandisan
SS object
•A ZPK object if no operand is an FRD or SS object and atleast one is an ZPK
object
•A TF object only if all operands are TF objects
Operations on systems of different types work as follows: the resulting type is
determinedbytheprecedence rules,andalloperandsarefirst convertedtothis
type before performing the operation.
Viewing LTI Systems As Matrices
In the frequency domain, an LTI system is represented by the linear input/
output map
This map is characterized by its transfer matrix H, a function of either the
Laplace or Z-transform variable. The transfer matrix H maps inputs to
outputs, so there are as many columns as inputs and as many rows as outputs.
If you think of LTI systems in terms of (transfer) matrices, certain basic
operations on LTI systems are naturally expressed with a matrix-like syntax.
For example, the parallel connection of two LTI systems
sys1 and sys2 can be
expressed as
FRD > SS > ZPK > TF
yHu=