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This thesis investigates scalable control design for networked dynamical systems, which are of great importance due to their wide range of practical applications, including large-scale formation control. A central challenge in such systems is enabling agents to coordinate effectively based only on local and relative information, particularly as the system size increases. To address this, the thesis develops a framework for designing robust and scalable coordination protocols that maintain performance even in large formations.

Paper I introduces serial consensus, a novel coordination protocol where the closed-loop system mimics the behavior of multiple simpler consensus protocols interconnected in series. This structure enhances robustness and stability. Paper II applies serial consensus to vehicular formations, demonstrating that it ensures string stability regardless of underlying communication topology. In Paper III, the scalable performance results are extended to the case of high-order coordination of agents with n^th-order dynamics (n ≥ 3). A consequence of this result is that formations of double integrators with local integral control can maintain scalable performance while rejecting constant load disturbances.

Paper IV proposes a class of scalable nonlinear consensus protocols based on the core idea of serial consensus, that is, serializing coordination. This enables coordination of a broader class of systems more closely linked to real-world applications. A unifying theme across Papers I–IV is the study of large-scale dynamical systems and their transient behavior—often in cases where traditional analysis would deem them unstable. To address this, Paper V develops new tools for performance analysis based on ε-pseudospectra, providing a theoretical foundation for understanding transient amplification and robustness in high-order networked systems. Together, these results contribute to a new understanding of design principles of scalable control and its implications for large-scale dynamical systems, offering new perspectives on stability, performance, and robustness in distributed control design.