Exponential uncertainty and quantization error: H₂ approach to networked control

Due to exponential uncertainty induced by uncertain network delays, the digital representation for continuous time invariant system becomes time varying, which adds difficulty to the analysis and synthesis of system. In order to overcome this difficulty, the exponential uncertainty is described as a polytopic model with bounded additive terms while quantization error is described as external disturbance. Utilizing structure information of polytopic model, we present a sufficient condition for networked control system to achieve the prescribed H₂ quantization error attenuation level with finite matrix inequalities instead of infinite ones. The attraction of the presented method is that linear matrix inequalities are presented to guarantee the constraint conditions for bounded additive terms in polytopic model, which are used in the controller design, so after obtaining the controller, controller parameters will satisfy these constraint conditions automatically and need not to be verified afterwards, which is very convenient for application.