Output tracking control of an aircraft subject to uncertainties in the dynamic model and additive state-dependent nonlinear disturbance-like terms is aimed. Uncertainties in the aircraft dynamic model yield an uncertain input gain matrix, which is neither positive definite nor symmetric and an uncertain term in the error dynamics. To deal with the uncertain input gain matrix, a decomposition method is utilized to put error dynamics in a form where an uncertain positive definite matrix multiplies the auxiliary error but this results in the control input to be pre-multiplied first with a unity upper triangular matrix which is uncertain and then with a known diagonal matrix. A novel controller composed of a neural network compensation term and an integral of signum of error is designed. A novel Lyapunov type stability analysis is utilized to prove global asymptotic tracking of output of a reference model. Extensive numerical simulations are presented to demonstrate the efficacy of the proposed controller where robustness to variation of initial states and a comparison with a robust controller are also shown.