Advanced dimensional analysis for robust control of benchmark structural system via generalized linear matrix inequalities

While development of control strategies for building systems has gained considerable attention in the field of structural and earthquake engineering, it remains a challenging task due to the complexity of the problem and the high computational costs involved. This paper presents a novel methodology that integrates dimensional analysis with generalized linear matrix inequalities (GLMIs) to design robust control strategies for benchmark building structures subjected to seismic excitations. By applying the Buckingham Π Theorem, the approach identifies key dimensionless groups, simplifying the representation of complex structural behavior and enabling systematic controller design even under significant uncertainties. The GLMI framework ensures robust performance across a variety of physical parameters, including mass, stiffness, and damping perturbations. The efficiency of the proposed methodology is demonstrated through numerical simulations on twenty-story high-rise benchmark steel structure inspired by the SAC project in Los Angeles, California. The study focuses on uncertainties in top-floor mass, and compares the performance of the proposed controllers with passive, and linear quadratic regulator (LQR) strategies. Results show that the presented control scheme achieves reliable seismic control by effectively handling parameter uncertainties while maintaining structural safety. This work provides a clear, systematic framework that balances technical rigor with accessibility, offering practical guidance for engineers and a comprehensive reference for researchers in advanced structural control.