ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

A new method for systems' stability analysis is presented. This method is called weight functions method and it replaces the problem of finding a Liapunov function with a problem of finding a number of functions (weight functions) equal to the number of first order differential equations describing the system. It is known that there are no general methods for finding Liapunov functions. The weight functions method is simpler than the classical method since one function at a time has to be found. This method’s conditions of solution stability and holonomic systems with dependent variables are analyzed. Also, applications such as the Lurie-Postnikov problem, stability of the rotational motion of a rigid body, the rigid body command stabilization are presented.