1. A New Control Framework
K0=V-1U is a nominal stabilizing controller for P0=M-1N. The transfer function from y to u is
K=(V-QN)-1(U+QM)
for some stable Q which is the parameterization of all stabilizing controller for P0=M-1N.
f=0 if the plant model is perfect (=0):
Tyr=P0K0(I+P0K0)-1
Q does not affect nominal tracking
disturbance rejection and robust stability are guaranteed by Q
Tyd=(I+P0K)-1 Tyu=K(I+P0K)-1
When plant is stable, take
N=P0, M=I
When K0 is minimum phase, take
U=I and V-1=K0 .

2. Fault Tolerant Control our approach
Conventional method: model the failures as model uncertainties and a robust worst case control design is done. Too conservative ! worst case is rare.
New method: Design K0=V-1U to satisfy the system performance by assuming no faults (and model uncertainties).
Design Q (using any robust techniques, fuzzy control methods, adaptive techniques, etc) to tolerate possible actuators and/or sensors failures (and model uncertainties).
Q can be made adaptive or be scheduled for different situations.
We believe every fault tolerant controller should be in this form.

3. Example: A Gyroscope simulation with one sensor fault
one input and two outputs system.
one sensor fault at 8 sec.
LQG controller becomes unstable with the sensor fault
H controller is robust but slow.
Our new controller performs exactly the same as the nominal LQG controller when there is no fault and maintains stability when there is a fault.

4. Experimental Study experiments with/without sensor fault
Our new controller (GIMC) performs closely to the LQG controller (K0). The difference is caused by the model uncertainties.
H controller fails to perform because of dead zone.
Without Sensor Fault at 2.2 sec.
System with LQG controller becomes unstable.
Our new controller performs well and maintains stability