Gain-scheduled H∞ control of two-dimensional discrete-time linear parametrically-varying systems

This paper addresses the design of gain-scheduled H_∞ control for two-dimensional discrete-time linear parameter-varying systems described by the Fornasini-Marchesini second local state-space model. The matrices of the system model depend affinely on time-varying parameters whose admissible values are assumed to belong to a given polytope. A method based on linear matrix inequalities is developed for designing a gain-scheduled static state feedback H_∞ controller where the controller gain is allowed to be affine, quadratic, or a matrix fraction of quadratic polynomial matrices in the scheduling parameters. The proposed control design is based on a Lyapunov function that can depend quadratically on the scheduling parameters.