Gain-scheduled control of LFT systems through duality and conjugate Lyapunov functions

In this paper, we study stability and performance properties of linear fractional transformation (LFT) parameter-dependent system using duality theory and tools from convex analysis. A pair of conjugate functions, the convex hull and the maximum of a family of quadratic Lyapunov functions, are used for analysis and synthesis LFT systems. A sufficient synthesis condition for gain-scheduled output feedback control problem is formulated as a set of linear matrix inequalities (LMI) with linear search over scalar variables. Finally, an example is used to demonstrate the advantages of the proposed approach