On the design of output feedback for finite and infinite pole assignment in singular systems with application to the control problem of constrained robots

For a given square solvable singular system Ex=Ax+Bu with output y=Cx we present a useful chain of transformations, acting on the quadruplet {E, A, B C}. The application of this chain enables the design of an output feedback for obtaining (provided the problem is solvable) finite and infinite pole assignment with regularity. Special consideration is given to the control problem of a holonomically constrained robot, and fundamental results concerning the singular model which is obtained by a (local) linearization of the equations have been established of the constrained mechanical system about a nominal trajectory. In particular we consider the structure of an output map which enables a simple closed-loop configuration for obtaining design objectives with regards to the resulting linear singular system.