Design of a controller for mechanical systems by the generalized energy function

Dynamics of the mechanical system is described by the matrix-second-order differential equation, and the coefficient matrices in the equation have some special properties such as symmetry and positivity. These properties should be reflected to the design method of controllers for mechanical systems. In this paper we discuss control problems of mechanical systems in the matrix-second-order differential equation model by paying attention to their potential and kinetic energy. First we introduce a concept called generalized energy function and then by using this new concept we discuss observability and controllability and propose a design method of feedback controllers of the mechanical systems.