(3.10)

i,j[!][1,N]^[!]
[!] ^{[!] :}

where Jis the NxNdiscrete system Jacobian, defined as

L

[!]k_i

L

O

J

=

O

Jrelates the change in Q_i+1over a single cycle to the applied perturbation scaling, K_i.

Figure 3.4 illustrates the relationship between the parameters of the linear model and the perturbed

system's cyclic motion in state space for a 1D system. In this example, the linear predictive model

is constructed using two sample points on Q_i+1= h(k), corresponding to applied perturbation

scalings of k₁and k₂.

Q_i+1.

The figure illustrates that we can predict (and hence control) the value of

Figure 3.4 - Linear parameters of a 1D discrete system in state space.
Here, [!]k= k₂- k₁