Causal observability of descriptor systems

Observability analysis for descriptor systems by using a matrix pencil approach is presented. Systems under consideration are the most general class of linear continuous descriptor systems. A few practically relevant notions of observability, particularly the causal observability which corresponds to the existence of a Luenberger observer and the corresponding necessary and sufficient test conditions, are provided. The interpretation of various observabilities in terms of matrix pencils offers insights into the physical meaning of these concepts.

[1]  P. Dooren.  The generalized eigenstructure problem in linear system theory , 1981 .

[2]  Frank L. Lewis,et al.  A tutorial on the geometric analysis of linear time-invariant implicit systems , 1992, Autom..

[3]  Andrzej Banaszuk,et al.  Remarks on observability of implicit linear discrete-time systems , 1990, Autom..

[4]  D. Cobb.  Controllability, observability, and duality in singular systems , 1984 .

[5]  Peter C. Müller,et al.  Observer design for descriptor systems , 1999, IEEE Trans. Autom. Control..

[6]  H. Rosenbrock.  Structural properties of linear dynamical systems , 1974 .

[7]  Leon O. Chua,et al.  Computer-Aided Analysis Of Electronic Circuits , 1975 .

[9]  R. F. Sincovec,et al.  Solvability, controllability, and observability of continuous descriptor systems , 1981 .

[10]  R. Newcomb.  The semistate description of nonlinear time-variable circuits , 1981 .

[11]  Ton Geerts,et al.  Regularity and singularity in linear-quadratic control subject to implicit continuous-time systems , 1992 .

[12]  L. Dai.  Impulsive modes and causality in singular systems , 1989 .

[13]  D. W. Fountain,et al.  Some generalized notions of observability , 1990, 29th IEEE Conference on Decision and Control.

[14]  N. Harris McClamroch,et al.  Singular systems of differential equations as dynamic models for constrained robot systems , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[15]  T. Kailath,et al.  A generalized state-space for singular systems , 1981 .

[16]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[17]  L. Silverman,et al.  System structure and singular control , 1983 .

[18]  P. Dooren.  The Computation of Kronecker's Canonical Form of a Singular Pencil , 1979 .

[19]  Andrew A. Goldenberg,et al.  Force and position control of manipulators during constrained motion tasks , 1989, IEEE Trans. Robotics Autom..

[20]  Ton Geerts.  Solvability conditions, consistency, and weak consistency for linear differential-algebraic equations and time-invariant singular systems: the general case , 1993 .

[21]  D. Luenberger.  Dynamic equations in descriptor form , 1977 .