Effects of using Observers on Stabilization of Uncertain Linear Systems

In this paper, the effects of using observers on robust linear state feedback controllers are studied. Lyapunov techniques are used to obtain estimate for important bounds (e.g., allowable uncertainty bounds and disturbance rejection bounds). In particular, sufficient conditions are obtained that, if met, guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback. We demonstrate how these conditions can be used to design observer based robust feedback controllers. Since almost full recovery of the uncertainty bound often requires high gain observers, we also study the effects of such observers on the disturbance rejection bounds and obtain an explicit condition for the trade-off involved. In particular, we show that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection. However, if there is only additive plant disturbance and no measurement disturbance, this degradation can be prevented.