Model reference tracking control for spatially interconnected discrete-time systems with interconnected chains

This study is concerned with the model reference tracking control problem for spatially interconnected systems (SISs) with interconnected chains in discrete-time case. The aim of this paper is to design a state-feedback controller such that the state of the controlled system tracks precisely a given stable reference signal or the output of the controlled system tracks the output of a given reference model well. First, two sufficient conditions are given to guarantee that the closed-loop system is asymptotically stable and the corresponding tracking performance requirement is satisfied, respectively. Next, the existence of the desired state-feedback controllers are obtained by the proposed methods based on linear matrix inequalities. Finally, a first-order partial differential equation simulation example is provided to illustrate the effectiveness of the derived methods.