An LMI-Based Cooperative Control Design Framework for the Bounded Exponential Consensus of Nonlinear Systems

In this paper we propose a new systematic methodology for the cooperative output feedback control design such that exponential consensus is achieved in a dual agent homogeneous nonlinear system network with additive control inputs. Our design approach ensures that all system trajectories are bounded and exponentially synchronize within a minimum and maximum decay-rate range. The results are derived by using a combination of two quasi-Linear Parameter Varying representations: one for the synchronization error dynamics and other for the absolute network dynamics. This way, we derive matrix inequality conditions that ensure both exponential consensus and absolute boundedness, which are used to design distributed controllers via convex optimization problems. The Lorenz Attractor is considered as a numerical example in order to illustrate the application of the proposed method.