Gain-scheduled H2 control of linear parameter varying systems using a parametric Lyapunov function

This paper deals with the problem of gain-scheduled H₂ control for linear parameter varying systems. The system state-space model matrices are affinely parameterized and the admissible values of the parameters and their rates of variation are supposed to belong to a given polytope. Based on a parameter-dependent Lyapunov function, a linear matrix inequalities methodology is proposed for designing a gain-scheduled state feedback H₂ controller, where the feedback gain is a matrix fraction of polynomial matrices with quadratic dependence on the scheduling parameters.