Distributed static output-feedback control for state synchronization in networks of identical LTI systems

This paper studies state synchronization of multi-agent systems with disturbances using distributed static output-feedback (OPFB) control. The bounded L-2 gain synchronization problem using distributed static OPFB is defined and solved. The availability of only output measurements restricts the local controls design, while the communication graph topology restricts global information flow among the agents. It is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded L-2 gain static OPFB. One condition is on the output measurement matrix on a local scale, and the other on the graph Laplacian matrix on a global scale. Under additional conditions a distributed two-player zero-sum game using static OPFB is also solved and leads to distributed Nash equilibrium on the communication graph. As a special case the static OPFB globally optimal control is given. A new class of digraphs satisfying the above condition on the graph Laplacian is studied. The synchronizing region for distributed static OPFB control is exposed and found to be conical, different than the infinite right-half plane synchronizing region for distributed state feedback. (C) 2015 Elsevier Ltd. All rights reserved.