Linking these two lines of research, this paper suggests total factor productivity growth as an ICAPM state variable
and further indicates that productivity risk exposure explains more than half of the one-month industry momentum profits.
Set pillar compression displacement u as the state variable
; then according to cusp catastrophe theory, the equation of the support system catastrophe model for equilibrium surface can be obtained (as shown in the following equation):
Once [??](t) stands for a set of unmeasured state variable
components, (17) can be interpreted as a state observer.
Using an additional state variable
which is in fact redundant, the optimality contract with hidden savings is presented in Section 5.
Step 5: Define State Variable
. Since the discrete large-signal state equations in (A.15), (A.16), and (A.21) have a high nonlinearity, control design technique based on the linear control theory cannot directly be applied.
Namely, [pi]( [[theta].sub.t+1]||[D.sub.t]) = [pi]([[theta].sub.t+1]|[[theta].sub.0:+1], [y.sub.1:t]) = [pi]([[theta].sub.t+1]|[[theta].sub.t]), where [pi](*) is probability density function and [[theta].sub.t] is the state variable
at time t.
[Q.sub.i] for i = 1, ..., 9 is the right-hand side of the differential equations of ith state variable
in system (1).
Input the initial state variable
, the desired state variable
, and the planning time.
where x(k) [member of] [R.sup.n] is the state variable
, u(k) [member of] [R.sup.m] and y(k) [member of] [R.sup.p] are the control input and output of the system (1), respectively, [A.sub.j] [R.sup.nxn], B [member of] [R.sup.nxm], and C [member of] [R.sup.pxn] are the state matrix, input matrix, and output matrix, respectively, and all matrices are constant matrices with appropriate dimensions.
Treating [T.sub.l] as a state variable
, the system can be described as follows:
in an effort to eliminate the state variable
[gamma] in favor of fr.