User`s guide

4 Arrays of LTI Models
4-28
where sys, the result of the operation, is an L TI array with the same array
dimensions as
sys1. You can use shortcuts for coding sys = op(sys1,sys2) in
the following cases:
• For operations that apply to LTI arrays,
sys2 doesnothavetobeanarray.
It can be a single LTI model (or a gain matrix) whose I/O dimensions satisfy
the compatibility requirements for
op (with those of each of the models in
sys1).Inthiscase,op applies sys2 to each model in sys1,andthekth model
in
sys satisfies
sys(:,:,k) = op(sys1(:,:,k),sys2)
• For arithmetic operations, such as +, *, /,and\,sys2 can be either a single
SISOmodel,or anLTIarrayof SISOmodels,evenwhen
sys1 is an LTI array
of MIMO models. This specia l case relies on MATLAB’s scalar expansion
capabilities for arithmetic operations.
- When
sys2 isasingleSISOLTImodel(orascalargain),op applies sys2
to sys1 on an entry-by-entry basis. The ijth entry in the kth model in sys
satisfies
sys(i,j,k) = op(sys1(i,j,k),sys2)
- When sys2 is an LTI array of SISO models (or a multidimensional array
ofscalar gains),
op applies sys2 tosys1 onan entry-by-entrybasisforeach
model in
sys.
sys(i,j,k) = op(sys1(i,j,k),sys2(:,:,k))
Examples of Operations on LTI Arrays with Single LTI Models
Suppose you want to create an LTI array containing three models, where, for
in the set , each model has the formτ
1.1 1.2 1.3
,,{}
H
τ
s
(
)
H
τ
s()
1
s τ+
-----------
0
1–
1
s
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=