To some theorists, the new results virtually guarantee the existence of other Earthlike worlds.
Sufficient conditions that guarantee the existence of the desired filter are also obtained.
There is again an important class of theorems that guarantee the existence of certain choices under appropriate hypotheses.
Conditions on Γ that will guarantee the existence, uniqueness, and continuity of solutions to the above equation are given.
These conditions guarantee the existence of an ellipsoid that contains the system state under zero initial conditions.
Based on this, sufficient conditions are given and proved to guarantee the existence of the robust fault detection filter system.
After that, conditions that guarantee the existence of periodic solutions surrounding the planned homoclinic orbits are derived.
Sufficient conditions are proposed which guarantee the existence of a Luenberger-like observer for the general system.
Then, variable structure controllers are designed to guarantee the existence of the sliding mode from the initial time.
A sufficient condition is provided to guarantee the existence of the discrete-time sliding modes in an LMI form.
While these constraints guarantee the existence of the inverse filters, their form is unconstrained and could be signal length dependent.
