Distributed State Feedback Control of Explicitly-Bounded Nonlinearly-Coupled Systems

The nominal linear subsystem state-space model having nonlinear couplings are used in this work. The quadratic dissipativity constraint approach, previously introduced and developed for the model predictive control of interconnected systems, is deployed herein with a static state-feedback strategy. We re-use the derivation for a quadratic bound on the nonlinear coupling in a newly derived stability condition for the decentralized excitation control of multiple-machine power systems. The state feedback gains are pre-computed from the LMI optimization problems formulated from this stability condition in combination with the open-loop dissipative condition for the global system and the closed-loop dissipative condition for subsystems. Inheriting the property of the non-monotonic decreasing Lyapunov function, the proposed decentralized static state-feedback approach is promising with non-conservative behaviours. The resulting static state-feedback gain can be used in the feedback policy for a distributed model predictive control scheme, when it is required to push the system towards tighter constraints for various economic objectives.