Distributed Observer-based LQ Controller Design and Stabilization for Discrete-time Multi-agent Systems

This paper will investigate the distributed observer-based LQ controller design and stabilization problem for uncoupled identical linear time-invariant multi-agent systems with a performance index coupling the behavior between the multi-agents. A design method is proposed by applying the decomposition of the global discrete-time algebraic Riccati equations. A computationally tractable solution can be obtained by solving four local algebraic Riccati equations which have the same dimensions as a single agent. The stability condition is given in terms of the spectrum of two matrices representing the desired sparsity pattern of the distributed controller and distributed observer. A limited overall performance can also be guaranteed by the proposed distributed controller which is parameterized by two scalars. To illustrate the effectiveness of the algorithm, a numerical example is provided.