Normal Form and Luenberger Observer for Linear Mechanical Descriptor Systems

Abstract

Normal forms are presented for linear mechanical systems with holonomic and/or nonholonomic constraints. These forms provide deep insight into the peculiar system structure of constrained linear mechanical systems or the so-called linear mechanical descriptor systems. Based on these normal forms, an explicit observer design method is proposed under a weaker observability assumption, i.e., finite observability or reachable observability on the linear mechanical descriptor systems. The observer has the Luenberger observer form and provides the estimation of displacements, velocities, and constraint forces simultaneously. The finite observability is shown to be a necessary and sufficient condition for the existence of this type of observer. The reason for the existence of the Luenberger observers for finitely observable linear mechanical descriptor systems is due to the special system structure. Two examples are included to illustrate the design method.