Abstract
Although we usually hope a system to be fully-actuated, unfully system often occur in practice, of which under actuated second-order systems are rather common in various applications, such as mechanical systems, robotics control, aircraft design, etc. In this paper, a direct parametric approach is proposed, solving the control problem of a class of under-actuated second-order system rather completely. According to the method in this paper, under proper assumptions, the under-actuated second-order nonlinear systems can actually be converted into a constant linear one satisfying desired eigenstructure. The method also further provides all the degrees of freedom in design which can be utilized to achieve other desired control performance. The solution of the problem is based on the solution to a type of second-order Sylvester matrix equations. Besides, the numerical example also shows the efficiency of the method.
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