\(H_{\infty}\) controller design for asynchronous multirate sampled-data systems (Q1719087)

Summary: This paper considers the analysis and synthesis of a linear discrete asynchronous multirate sampled-data system. An \(H_{\infty}\) controller based on an observer is proposed, which guarantees the stability of the closed system and makes the \(H_{\infty}\) norm of the closed system less than a given attenuation level. To improve the performance further, a tradeoff strategy is applied. That is, the exogenous signals sampled at different rates are lifted to an appropriate signal rate, while the endogenous signals are not lifted for avoiding the causal constraint and the dimension multiplied again. The controller is obtained by solving the corresponding matrix inequality, which can be calculated by Matlab. Finally, an example is presented to demonstrate the validity of these methods.