H_∞ Control for Observer-Based Non-Negative Scaled Edge Consensus of Continuous-Time and Discrete-Time Networked Systems

This article studies the observer-based non-negative scaled edge-consensus (NNSEC) problems for continuous-time and discrete-time networked systems, and then these problems are extended to the cases with input saturation. Specifically, two observer-based algorithms are proposed by using only the outputs of neighboring edges, and the mathematical expressions of the control gain matrix and observer gain matrix in the two algorithms are derived. Based on the $H_{\infty }$ control theory and low-gain feedback technique, the observer gain matrix and control gain matrix can be obtained to achieve the NNSEC of continuous-time cases, and for discrete-time cases, the NNSEC can be achieved if the control gain matrix and observer gain matrix are nonpositive. Finally, four examples are proposed to verify the effectiveness of the main results.