Gain-scheduled ℋ2 controller synthesis for linear parameter varying systems via parameter-dependent Lyapunov functions

This paper deals with the problem of gain-scheduled ℋ︁2 control for linear parameter-varying systems. The system state–space model matrices are affinely parameterized and the admissible values of the parameters and their rate of variation are supposed to belong to a given convex bounded polyhedral domain. Based on a parameter-dependent Lyapunov function, a linear matrix inequality methodology is proposed for designing a gain-scheduled state feedback ℋ︁2 controller, where the feedback gain is a matrix fraction of polynomial matrices with quadratic dependence on the scheduling parameters. Copyright © 2005 John Wiley & Sons, Ltd.