H∞ Guaranteed Cost Tracking Control With Preview for a Class of Discrete‐Time One‐Sided Lipschitz Singular Systems

This paper investigates the design of an guaranteed cost (GC) tracking controller with preview capabilities for discrete‐time nonlinear singular systems. Specifically, the system nonlinearity is assumed to satisfy one‐sided Lipschitz (OSL) and quadratically inner bounded (QIB) constraints. To ensure zero steady‐state tracking error, the original tracking task is converted into an admissibilization problem by constructing an augmented error system (AES) via the forward difference scheme, which integrates system states, error dynamics, and future reference information. By leveraging the differential mean value theorem (DMVT) combined with decoupling techniques and slack matrix variables, we derive new sufficient conditions that ensure that the closed‐loop system is admissible while achieving prescribed disturbance attenuation and cost efficiency. A unified design framework is presented for both state and static output feedback controllers, with solvability conditions cast as Linear Matrix Inequalities (LMIs). Finally, simulation results validate the effectiveness and performance superiority of the proposed preview control strategy.