Almost disturbance decoupling problem with internal stability via state or measurement feedback-singular perturbation approach

An almost disturbance decoupling technique guaranteeing internal stability of a linear system while using either state feedback or only measurement feedback is considered. Under a set of necessary and sufficient conditions, a state feedback controller is explicitly constructed. Similarly, a full or reduced-order observer-based measurement feedback controller is explicitly constructed under a set of necessary and sufficient conditions. Both the developed controllers guarantee the asymptotic stability of the closed-loop system in the absence of disturbances. Furthermore, they can reduce, for example, the H_∞ norm of the transfer function from the external disturbance to the controlled output to any arbitrarily specified value. Unlike other methods which merely give the solvability conditions, this method explicitly constructs them. This is a `one shot´ design and it does not encounter arbitrarily small or large numbers; hence, it is not plagued by `stiffness´ or any other numerical stability problems. The algorithm has been implemented in a `Matlab´ software package