H2 controller design of linear systems with time-varying uncertainties and input quantization

The paper considers the robust H₂ state feedback control design for a class of linear uncertain systems with input quantization. The uncertainties are assumed to be time-varying, unknown, but bounded. The state feedback controller includes two parts. The first part, u₁(t), whose gains updating automatically between the lower bounds and upper bounds of uncertain parameters, is obtained according to linear matrix inequalities conditions. Such design purpose is to guarantee the robust stability and H₂ performance. The second part, u₂(t) is designed to eliminate the effect of the quantization error. The main feature of this paper is that a switching mechanism is introduced effectively to determine which bound of uncertain parameters is active in the process of control at each time instant. Finally, a numerical example is given to demonstrate the effectiveness of the proposed scheme.