Graph Laplacian Based Novel Decentralized Control for Robust Stabilization and $L_{2}$ Gain Analysis of Nonlinear Interconnected Systems

In this paper, a Graph Laplacian based novel decentralized controller design is proposed for robust stabilization and
$L_{2}$
gain analysis of a class of nonlinear interconnected systems via static output feedback control within the LMI framework. This large-scale system is composed of linear subsystems coupled by nonlinear time-varying interconnections satisfying quadratic constraints. The proposed controller uses the information based on the Laplacian matrix of the graph to design a decentralized controller that operates based on local information available at each subsystem. An LMI approach is sufficiently proposed as a feasibility problems of a BMI with respect to controller gains via static output feedback structure. The simulation results show that the proposed controller can effectively stabilize the nonlinear interconnected systems and achieve desired performance, even in the presence of disturbances and uncertainties. The proposed controller has potential applications in various fields, such as robotics, control systems, and networked systems.