13

Bounds (proof)

q**Proof:** Consider

where
(*A,B*) is controllable and (*C,A*) is observable.

Integration
from *t= -**¥** *to* t = 0* with *x(-**¥* *)=0* and *x(0)
= x**0* gives

Given *x(0) = x**0* and *w* = 0 for* t**³*0, the norm of *z(t)=Ce**At **x**0* can be found from