Semiglobal Cluster Consensus for Heterogeneous Systems with Input Saturation

In this article, the semiglobal cluster consensus problem is investigated for heterogeneous generic linear systems with input saturation. A general case in a leaderless framework is studied first, and then in order to broaden the scope of application, we consider a special case in which the leader nodes are pinned intermittently. To tackle the above problems, we propose a linear control scheme by using the low-gain feedback technique under the assumptions that each node is asymptotically null controllable and the underlying topology of each cluster (the extended cluster under the intermittent pinning control) has a directed spanning tree. The Lyapunov-based method and the low-gain feedback technique are developed for convergence analysis. It is shown that for both cases, the convergence rate is explicitly specified, which depends on the low-gain parameter and system matrices. Finally, two numerical examples are provided to verify the effectiveness of the theoretical findings.