Guaranteed cost control for rational parameter-dependent discrete-time systems

Presents an LMI method for designing static output feedback controllers with a guaranteed H₂ performance for a class of discrete-time linear systems with either rational or polynomial parameter dependence. The parameters and their rate of variation are assumed to be bounded by a given polytope. Stability as well as an H₂ performance bound are ensured via a rational parameter-dependent Lyapunov function. The method can be used to design robust controllers, linear parameter varying controllers, and non-fragile controllers with prescribed ranges of errors that can be tolerated in the implementation of the designed controller gains. An extension of the proposed result to the case where the controller gains are required to satisfy certain structure constraints, such as in decentralized control, is also discussed.