Local stabilisation of uncertain linear time-invariant plant with bounded control inputs: parametric H∞ loop-shaping approach

In this study, an attempt has been made to design an output feedback controller for local stabilisation of uncertain linear time-invariant plant with bounded control inputs. The design is accomplished via parametric H_∞ loop-shaping control by describing the uncertainty as perturbations to normalised coprime factors of the shaped plant. The shaped plant is designed based on the closed-loop design specifications by appropriately choosing the weighting transfer function matrices. For the existence of stabilising controller, a set of sufficient conditions has been derived in linear matrix inequality framework and subsequently, a region of attraction is estimated such that the control inputs never exceed the pre-specified bounds. To illustrate the effectiveness of the proposed method, a numerical example has been elucidated.