Stabilization of Linear Hyperbolic Systems of Balance Laws with Measurement Errors

International audienceThis chapter considers the feedback stabilization of partial differential equations described by linear balance laws when the measurements are subjected to disturbances. Compared to our previous work on robust stabilization of linear hyper-bolic systems, the presence of source terms in the system description complicates the analysis. We first consider the case of static controllers, and provide conditions on system data and feedback gain which result in stability of the closed-loop system, and robustness with respect to measurement errors. Motivated by the applications where it is of interest to bound the maximum norm of the state trajectory, we also study feedback stabilization with dynamic controllers. Conditions in terms of matrix inequalities are proposed which lead to robust stability of the closed-loop system in the presence of measurement errors in the feedback. As an application, we study the problem of quantized control, where the quantization error plays the role of disturbance in the measurements. The simulations for an academic example are reported as an illustration of our theoretical results