NORMAL-FORM AND LUENBERGER OBSERVER FOR LINEAR MECHANICAL DESCRIPTOR SYSTEMS

Normal forms are presented for linear mechanical systems with holonomi c and/or nonholonomic constraints. These forms provide deep insight in to the peculiar system structure of constrained linear mechanical syst ems or the so-called linear mechanical descriptor systems. Based on th ese normal forms, an explicit observer design method is proposed under a weaker observability assumption, i.e., finite observability or reac hable observability on the linear mechanical descriptor systems. The o bserver has the Luenberger observer form and provides the estimation o f displacements, velocities, and constraint forces simultaneously. The finite observability is shown to be a necessary and sufficient condit ion for the existence of this type of observer. The reason for the exi stence of the Luenberger observers for finitely observable linear mech anical descriptor systems is due to the special system structure. Two examples are included to illustrate the design method.