Quadratic L2-gain performance linear parameter-varying realisation of parametric transfer functions and state-feedback gain scheduling control

The study deals with the quadratic L2-gain performance linear parameter-varying realisation of parametric transfer functions and state-feedback gain scheduling control. It is shown that any parametric transfer function, which has L2-gain performance with a bound for all constant parameters values, admits a state space realisation guaranteeing quadratic L2-gain performance with the bound under arbitrary parameter variations. A reasonably general procedure is provided to find such a realisation with linear matrix inequality optimal technique. Furthermore, according to the realisation, the state-feedback gain scheduling control design is also dealt with. Finally, a simple numerical example is given to illustrate the efficiency of the proposed method.