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Direct adaptive control for nonlinear matrix second-order systems with time-varying and sign-indefinite damping and stiffness operators

A direct adaptive control framework for a class of nonlinear matrix second-order systems with time-varying and sign-indefinite damping and stiffness operators is developed. The proposed framework guarantees global asymptotic stability of the closed-loop system states associated with the plant dynamics without requiring any knowledge of the system nonlinearities other than the assumption that they are continuous and bounded. The proposed adaptive control approach is used to design adaptive controllers for suppressing thermoacoustic oscillations in combustion chambers.