For specific Lyapunov based disturbance cancellation methods i would suggest you the works regarding " Output Regulation of Nonlinear Systems" . The o/p reg. problem deals with disturbance rejection for nonlinear systems. You can follow the works of "Hassan K Khalil" and "Attaullah Memon" on these topics.

I personally would suggest you to read "Arie Levant " his works on Higher Order Sliding mode control are very good and easy to implement. I have studied and implemented them and they produce good results for dist. Rejection and tracking references. 

Hi Salman:

Lyapunov's approach to deal with the disturbance rejection in nonlinear systems is not the only way to counteract the adverse effects which could cause such disruption in the stability and / or system performance.

I recommend that you will revise the work done several years ago by Dr. Gao and his colleagues, whose area of research is related to the active disturbance rejection control (ADRC).

Either way, I append to this comment a related article with what you are investigating, hoping you find it useful. I'll also add some publications on active disturbance rejection which can be found here on ResearchGate.

Best regards from Oaxaca, Mexico

Chapter State Observers for Active Disturbance Rejection in Inductio...

Conference Paper A survey on active disturbance rejection control

Article Active Disturbance Rejection Control of a Magnetic Suspension System

Please refer to these articles:

https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller

https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance

https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design

Article From PID to Nonlinear State Error Feedback Controller

Article Improved Sliding Mode Nonlinear Extended State Observer base...

Article On the Improved Nonlinear Tracking Differentiator based Nonl...

Please refer to this article:

https://www.researchgate.net/publication/318726178_An_Improved_Active_Disturbance_Rejection_Control_for_a_Differential_Drive_Mobile_Robot_with_Mismatched_Disturbances_and_Uncertainties

Conference Paper An Improved Active Disturbance Rejection Control for a Diffe...