Guaranteed cost sampled-data control: An input delay approach

In this paper, the problem of robust guaranteed cost sampled-data control is investigated for a linear system with norm bounded time-varying parametric uncertainties. By applying an input delay approach, the system is transformed into a continuous time-delay system. Using the Lyapunov stability theory and linear matrix inequality (LMIs) method, a robust guaranteed cost sampled-data control law is derived to guarantee that the asymptotical stability of the closed-loop system and the quadratic performance index less a certain bound for all admissible uncertainties. Sufficient conditions for the existence of state-feedback controller are obtained in the form of linear matrix inequalities (LMIs). A convex optimization problem is formulated to obtain the optimal state-feedback controller which can minimize the quadratic performance level. The effectiveness of the proposed method can be illustrated by the simulation example.