Guaranteed Cost Control for Uncertain Discrete-time Systems with State and Input Delays

The problem of guaranteed cost control for norm bounded uncertain discrete-time systems with both state and input delays is studied. Delay-dependent conditions for the existence of the guaranteed cost controller are developed by introducing two zero formulas and some free weighting matrices in the forward difference of Lyapunov functional. The mathematical development avoids the model transformation and the bounding cross-terms which often lead to the conservatism of the criterion. As the conditions are not expressed in terms of strict linear matrix inequalities form, an iterative algorithm is proposed to solve the non-convex feasibility problem. Thus, desired guaranteed cost controller can be constructed. A numerical example is given to demonstrate the effectiveness of the proposed method.