k minus 1 Baseline right-parenthesis comma bold u Subscript k Baseline right-parenthesis 4th Row bold g left-parenthesis bold x Subscript k Baseline comma bold u Subscript k Baseline right-parenthesis EndMatrix period"/>
Let denote the th composite of the system function as:
(3.10)
Given an initial state and the sequence , the corresponding sequence of predicted outputs is obtained as:
(3.11)
To simplify the notation, let us define such that
(3.12)
then we have:
Defining
(3.13)
the filtered state estimate is computed from the following discrete‐time system [9]:
(3.14)
(3.15)
where is the observer gain, , and is the discrete nonlinear observability matrix, which is computed at sample time as:
(3.16)
The observer gain is determined in a way to guarantee local stability
