Decentralized stabilization of symmetric systems with delayed observer-based feedback

This paper examines decentralized observer-based stabilization for symmetric interconnected systems. The structure of these systems is composed of identical subsystems with symmetric interconnections. Linear time-invariant dynamic systems are considered within the continuous-time case. The observer inputs operate with a delayed system output. Single as well as multiple time-varying interval bounded delays in the loop are considered. The state space matrices of these systems are decomposable into block diagonal matrices. Their properties and a robust stabilization approach are used to construct the design model which is subsequently used for the gain matrices selection by using Linear Matrix Inequalities. The main result shows that when these gain matrices are implemented into the overall system as local controller-observers, then the entire closed-loop system guarantees asymptotic stability. An application example illustrates the effectiveness of this method.