We propose an algorithm to estimate whole-brain effective connectivity measures by integrating structural connectivity matrix between brain regions and resting-state functional MRI data. Our algorithm first uses the Lyapunov inequality from control theory to ensure that the estimated whole-brain dynamic system is stable and physically meaningful. Then, the effective connectivity measure is characterized by a novel conditional causality measure. We applied the proposed algorithm to a public dataset which consisted of healthy controls (n=94), patients with schizophrenia (n=45), bipolar (n=44) and ADHD (n=37). Our results show that the proposed approach provides reliable estimation brain-network features of these brain disorders.