73
A new performance index is taken as
0 = 1 Cfr'(t)QS(t) + tr* (t)R(t)]dt (4-58)
o
The standard algebraic Riccati equation may be solved yielding an
optimal feedback gain K for the system (4-56). It just so happens that
if this same feedback gain is used for the original system then the
integrand of (4-55) is minimized with respect to the original system.
In addition, the eigenvalues of the closed-loop system will all have
real parts less than -a. This is the desired result. A similar
technique can be used in discrete-time control [21].