H∞ control for uncertain discrete-time system with data packet dropouts and one step delay

For a class of uncertain discrete-time system with date packet dropouts and one step delay, a state feedback H∞ controller design is studied in this paper. The data packet dropouts meet with the known probability of Bernoulli distribution. A state feedback controller is designed to make the entire loop-closed system satisfy the mean square exponential stability and specified performance indicators. Sufficient conditions are derived for the existence of controller. The parameters of the controller are obtained by solving the linear matrix inequalities. A numerical example is also provided to demonstrate the validity of the proposed design scheme.