This thesis investigates robust distributed formation control algorithms for multi-agent
systems (MAS), addressing critical challenges such as model uncertainties, input delays,
external disturbances, and measurement noise. Combining approaches from three related
studies, this work introduces a cohesive framework based on linear matrix inequalities (LMI)
to develop distributed control strategies that guarantee stability, robustness, and accurate
formation tracking in real-world applications such as robotics, autonomous systems, and
networked control. First, the problem of input delay and model uncertainty is tackled using
a predictor-based control scheme, exploiting the finite spectrum assignment (FSA) technique
to mitigate the effects of delays. The approach simplifies the multi-agent formation
problem into a single-agent stability analysis, with controller and predictor gains derived via
LMIs to maximize the allowable perturbation bound under delays. Additionally, practical
digital implementation aspects are explored, providing insights into stability preservation
in discrete-time realizations. Next, a mixed H2/H&infin performance-based formation tracking
controller is introduced to enhance robustness against disturbances and measurement noise.
This controller optimally balances performance and disturbance attenuation, ensuring
accurate formation tracking under directed topologies. The control synthesis is formulated
as an LMI problem, offering a systematic method for tuning performance and robustness
trade-offs. Further, extending the robust control framework, a consensus strategy is
developed for descriptor-type multi-agent systems, where agents exhibit singular dynamics.
A distributed observer-based consensus protocol is designed to handle model uncertainties.
By transforming the consensus problem into an equivalent single-agent stability framework,
stability conditions are derived using LMI formulations, ensuring scalability and resilience in
uncertain environments. Theoretical contributions are validated via numerical simulations
in MATLAB, demonstrating enhanced robustness, disturbance rejection, and adaptability
to delays, disturbances, and uncertainties. The results underscore the efficacy of LMI
techniques in advancing distributed formation control for complex, real-world multi-agent
applications.