Specifications

Operations on LTI Arrays
5-27
dimensions as sys1. You can use shortcuts for coding sysa = 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
sysa(:,:,k) = op(sys1(:,:,k),sys2)
•For arithmetic operations, such as +, *, /,and\, sys2 can be either a single
SISOmodel,oranLTIarrayofSISO models,evenwhen
sys1 isanLTIarray
of MIMO models. This special case relies on MATLAB’s scalar expansion
capabilities for arithmetic operations.
- When
sys2 is a single SISO LTI model (or a scalar gain), op applies sys2
to sys1 on an entry-by-entry basis. Theijth entryin the kth model insysa
satisfies
sysa(i,j,k) = op(sys1(i,j,k),sys2)
- When sys2 is an LTI array of SISO models (or a multidimensional array
of scalar gains),
op appliessys2 to sys1 onan entry-by-entry basis for each
model in
sysa.
sysa(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 form
You can do this efficiently by first setting up an LTI array
h containing the
SISO models and then using concatenation to form the LTI array
H of
MIMO LTI models , . To do this, type
tau = [1.1 1.2 1.3];
for i=1:3 % Form LTI array h of SISO models.
τ
1.1 1.2 1.3
,,{}
H
τ
s
(
)
H
τ
s
()
1
s
τ
+
-----------
0
1–
1
s
---
=
1 s τ+(
)
⁄
H
τ
s(
)
τ 1.1 1.2 1.3,,{}∈