Robust control for structural systems with structured uncertainties

This paper develops a robust active control approach to treat structured uncertainties in system, control input, and disturbance input matrices based on an uncertain structural system. Special single value decomposition is applied to all structured uncertain structures. In addition, unstructured uncertainties in the disturbance input matrix are also considered along with other structured uncertainties. Robust active control provides both robust α-degree relative stability and H_∞ disturbance attenuation. The H₂ norm of the transfer function from the external disturbance forces to the observed system states is restricted by a prescribed attenuation index. Considered uncertainties are both structured uncertainties and norm-bounded unstructured uncertainties, especially structured ones. The preservation of robust H₂ optimality of uncertain structural systems is discussed. Numerical simulations for an uncertain building model excited by the 1940 El Centro, California, earthquake data are described. Results may be applied to robust control analysis and design of structural systems