Error-constrained reliable tracking control for discrete time-varying systems subject to quantization effects

In this paper, the reliable tracking control problem based on set-membership idea is investigated for the discrete time-varying systems subject to time-delays, quantization effects and parameter uncertainties. The failures of actuators are quantified by a variable varying in a given interval. The norm-bounded uncertainty enters into the system matrices, and the quantizer is assumed to be of the logarithmic type, as well as the measurement noises and process noises are formulated as unknown but bounded and confined in ellipsoidal sets. The aim of the addressed reliable tracking control problem is to design an observer-based controller, such that, for the admissible time-delays, uncertainties, unknown but bounded noises, quantization effects and actuator failures, both the tracking error and the estimation error are not more than certain upper bounds that can be minimized at each time instant. Several sufficient conditions for the existence of observers and reliable controllers are derived in terms of the solutions to certain matrix inequalities that can be solved effectively by using available software. Finally, a simulation practical example is employed to show the effectiveness of the proposed design scheme.