Almost output regulation for parameter-dependent linear fractional transformation systems

An important problem of output regulation for linear fractional transformation (LFT) systems is considered. This problem is mainly concerned about tracking and/or rejection of persistent signals produced by some external generator. Necessary and sufficient solvability condition for LFT systems as two linear matrix equations, which is an extension of the existing output regulation results for the linear time invariant and nonlinear systems will be presented. On the basis of the analysis condition, the LFT almost output regulation problem of approximately tracking/rejecting persistent signals will be studied by minimising the Lscr₂ gain from perturbation of the signal to error output. Its synthesis condition will be formulated as two matrix equations plus a set of linear matrix inequalities. An example will be used to demonstrate the proposed approach.