TABLE OF CONTENTS Basically, there are two approaches to design LPV gain-scheduled controllers. One of them is based on a scaled version of the small gain theorem [5, 58, 68, 70]. This approach, which can be applied to LPV systems with fractional parameter dependence, is called LFT gain scheduling technique. It consists in reformulating the gain scheduling task as a robust performance problem with a special plant/uncertainty structure. The other approach, called quadratic gain scheduling, is based on Lyapunov theory [4, 6, 9, 95]. This approach is applicable to any LPV system. In the sequel, we limit our exposition to quadratic gain scheduling techniques since we only use them in this book for the design of wind turbine controllers. The interested reader will find a detailed description of LFT gain scheduling techniques in [5, 58, 68, 70].
Consider an open-loop LPV system with state-space realisation of the form
where x( t) ? 
is the state, w ? 
the disturbance, u( t) ? 
the control input, z( t) ? 
the error, y( t) ? 
the measured variable, and ?( t) ? 
the scheduling parameter. The signals w( t) and z( t), which usually are the input and output of the weighting functions, are chosen according to the performance specification. As in any gain-scheduled controller, the scheduling variable ?( t) is assumed...
