A Unified Analytical and Computational Approach for Stability Analysis in Complex Networked Systems

Abstract

Complex networked systems stability analysis has become a crucial task in contemporary engineering applications and systems such as cyber-physical systems, multi-agent networks, and enormous interconnected infrastructures. Traditional analytical tools offer theoretical assurances but in many cases, they cannot be scaled, whereas computational tools are more flexible but with little formal justification. This gap is bridged by the present paper, which suggests a single analytical and computational framework of stability analysis in complex networked systems. The framework combines the theory of Lyapunov-based stability with the effective use of numerical simulation tools to extract factors of stability and to allow scalable validation. Generalized networked dynamical system model is developed based on graph-theoretic principles and stability criteria based on systematic analysis methods are formulated. This can be integrated into a series of computations, which are run with iterative solvers and convergence checks to achieve a consistency between theory and simulation. Little and large-scale networks Numerical experiments show that the accuracy, convergence, and robustness of the method are better than currently used methods. The given method can be easily extended to the different network structures and system parameters. This standard framework offers a stable and scalable stability assessment device in smart grid use and IoT systems, distributed control networks, and additional data-driven and real-time automation in the future.