Observer design for linear time varying descriptor systems: numerical algorithms

Examines the design of observers for linear time varying descriptor systems for which the observer estimates are also physically correct in that they satisfy the same constraints as the solutions of the descriptor system. Careful attention is paid to ensuring that all quantities are computable by numerical algorithms. One way to implement this approach is fully developed. A computational example is given.

[1]  R. Nikoukhah,et al.  Observer Design for Linear Time Varying Descriptor Systems , 1997 .

[2]  B. Leimkuhler,et al.  Numerical solution of differential-algebraic equations for constrained mechanical motion , 1991 .

[3]  Stephen L. Campbell,et al.  Solvability of General Differential Algebraic Equations , 1995, SIAM J. Sci. Comput..

[4]  D. Mayne,et al.  Design issues in adaptive control , 1988 .

[5]  Stephen L. Campbell,et al.  Uniqueness of completions for linear time varying differential algebraic equations , 1992 .

[6]  Stephen L. Campbell,et al.  Automatic Differentiation and Implicit Differential Equations , 1999 .

[7]  V. Mehrmann,et al.  Smooth factorizations of matrix valued functions and their derivatives , 1991 .

[8]  S. Campbell.  Linearization of DAEs along trajectories , 1995 .

[9]  M. Ikeda,et al.  Stabilization of Linear Systems , 1972 .

[10]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[11]  The output-nulling space, projected dynamics, and system decomposition for linear time-varying singular systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[12]  Peter C. Müller,et al.  Normal Form and Luenberger Observer for Linear Mechanical Descriptor Systems , 1993 .

[13]  R. Nikoukhah.  A new methodology for observer design and implementation , 1998, IEEE Trans. Autom. Control..

[14]  W. J. Terrell,et al.  Duality, observability, and controllability for linear time-varying descriptor systems , 1991 .

[15]  S. Campbell,et al.  Observability of linear time-varying descriptor systems , 1991 .

[16]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[17]  C. D. Meyer,et al.  Generalized inverses of linear transformations , 1979 .

[18]  D. N. Shields,et al.  Partial Singular-Value Assignment in the Design of Robust Observers for Discrete-Time Descriptor Systems , 1988 .

[19]  P. Kabamba,et al.  Observation and Estimation in Linear Descriptor Systems With Application to Constrained Dynamical Systems , 1988 .

[20]  Stephen L. Campbell,et al.  A general form for solvable linear time varying singular systems of differential equations , 1987 .