Guaranteed cost gain-scheduled control of two-dimensional discrete-time linear parameter-varying systems

This paper deals with gain-scheduled control of two-dimensional discrete-time linear parameter-varying systems described by a Roesser state-space model with matrices depending affinely on scheduling time-varying parameters that evolve in a convex-bounded polyhedral domain. A method is proposed for designing static state feedback gain-scheduled controllers with a guaranteed quadratic regulator-type performance. The control design builds on a Lyapunov function which is allowed to be quadratic in the scheduling parameters, and is tailored via a finite set of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed control design method.