This monograph examines stability in complex distributed parameter systems using advanced robust control methods. It presents Lyapunov-based conditions in the form of linear matrix inequalities to establish the stability analysis for the case of constrained control, sampled-data control, event-triggered control, and disturbance rejection control. The book offers innovative strategies to tackle issues related to nonlinearity, uncertainties, and delays. The theoretical contributions of this work are significant, providing valuable insights that extend beyond academic theory into practical engineering applications. The methods discussed are poised to influence real-world problem-solving in this field. The insights and methods presented will be invaluable to both researchers and practitioners, offering a deeper understanding of the impacts of time delays and advanced control techniques.