Design for H ∞ almost disturbance decoupling problem with internal stability via state or measurement feedback—singular perturbation approach

Abstract

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. All the developed controllers guarantee the asymptotic stability of the closed-loop system in the absence of disturbances. Furthermore, they can reduce 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, our method explictly constructs them. Also our controllers are parametrized in terms of tuning parameters, by the tuning of which the disturbance reflected in the output can be attenuated to any desired degree of accuracy