A Polynomial Decentralized Controller Design for a Large-Scale Nonlinear System: SOS Approach

This paper proposes a novel approach for designing a decentralized controller to stabilize the large-scale nonlinear system. Unlike the previous studies, the polynomial system framework is employed to model the nonlinear large-scale system to decrease not only the modeling error but also the complexity and computational load significantly. Especially, in case the large-scale nonlinear systems consist of non-polynomial forms (such as sine, cosine, and so on), synthesizing the controller for this system becomes much more challenging. By putting non-polynomial terms inside the matrices, a new approach for designing a decentralized polynomial controller is presented to eliminate the impacts of nonlinear terms and stabilize the system. Based on Lyapunov methodology, the conditions for synthesizing a decentralized polynomial controller expressed under the framework of Sum-of-Square (SOS) are derived in the main theorems. Finally, the effectiveness and superiority of the proposed method are demonstrated in two illustrative examples.