Exponential stabilisation of state-delay systems

The exponential stabilisation problem of a class of dynamical systems with time delay and mismatched uncertainties is considered. The structure of the uncertainties is affinely bounded. The time delay factor could be variable or of constant value. In the case when the time delay is variable, it is established that state-feedback controllers can be constructed to render the closed-loop system exponentially asymptotically stable. Several published results are then derived as special cases. The important case of constant delay is further examined using one-term and two-term state-feedback controllers. A simulation example of a water-quality model is given to illustrate the effectiveness of the proposed control schemes.