The paper proposes a decentralized excitation controller to improve the stability of large power systems. Extended Lyapunov-like energy function and equivalent expressions of stator transient voltages are utilized to design a nonlinear adaptive excitation controller. The proposed controller only requires local machine measures and parameters. The performance of the designed excitation control system is evaluated on the wellknown IEEE 118-bus 54-unit power system and compared with conventional exciter controls. Index Terms-Multi-machine power systems, automatic voltage control, structure preserving model, transient stability analysis, decentralized control, Lyapunov function. NOMENCLATURE SPM Structure preserving model. RNM Reduced-network model. AEC Adaptive excitation controller. RNC RNM-based excitation controller. m Number of machines. b Number of buses. l, k, pjq Index of (machine) bus. Ω l Index set of buses which connect to bus l. Ω Index set of branches, k P Ω l ñ lk P Ω. b, pmq Index set of (machine) buses,m Ďb. Z 0 Equilibrium value of any variable Z. 9 Z Time derivative of any variable Z. Hessp¨q Hessian matrix of a function. V t l Voltage magnitude of bus l, in pu. V Voltage magnitude vector. θ l Voltage angle of bus l, in rad. θ Voltage angle vector. δ j Power angle of jth machine, in rad. δ Power angle vector. δ j , θ lk Relative anglesδ j " δ j´θj , θ lk " θ l´θk. V dj , V qj V dj "´V tj sinδ j , V qj " V tj cosδ j. V sj ,Ṽ cjṼsj " V dj0´Vdj ,Ṽ cj " V qj´Vqj0. ω j Relative speed of jth machine, in rad/s. ω Relative speed vector.