In-Domain Stabilization of Block Diagonal Infinite-Dimensional Systems With Time-Varying Input Delays

This article is concerned with the in-domain stabilization of a class of block diagonal infinite-dimensional systems in the presence of an uncertain and time-varying delay in the distributed control input. Two actuation schemes are considered. The first one assumes a control input that is fully distributed over the domain. The second one assumes that the control input is finite-dimensional, acting over the domain via a bounded operator. In both cases, the control design strategy consists in a predictor feedback law synthesized on a finite-dimensional truncated linear time invariant (LTI) model capturing the unstable dynamics of the original infinite-dimensional system. The predictor feedback law is designed based on the knowledge of the nominal value of the uncertain and time-varying input delay. In the second actuation scheme, the case of distinct input delays in the different scalar control input channels is considered.