Impulse observability and impulse controllability of linear time-varying singular systems

Impulse controllability and impulse observability of linear time-varying singular systems in a standard canonical form are examined. We focus on the fast subsystems with constant-rank N matrices. Sufficient and necessary conditions are derived and presented directly in terms of system parameters. Conditions obtained for these two properties are algebraically dual to each other.

[1]  Chi-Jo Wang.  Controllability and observability of linear time varying singular systems , 1999, IEEE Trans. Autom. Control..

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

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

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

[5]  Volker Mehrmann,et al.  Regularization of Linear Descriptor Systems with Variable Coefficients , 1997 .

[6]  Chi-Jo Wang,et al.  State feedback impulse elimination of linear time-varying singular systems , 1996, Autom..

[7]  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.

[8]  Werner Rath,et al.  Derivative and proportional state feedback for linear descriptor systems with variable coefficients , 1997 .

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

[10]  Volker Mehrmann,et al.  The linear quadratic optimal control problem for linear descriptor systems with variable coefficients , 1997, Math. Control. Signals Syst..

[11]  Linda R. Petzold,et al.  CANONICAL FORMS AND SOLVABLE SINGULAR SYSTEMS OF DIFFERENTIAL EQUATIONS , 1983 .

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

[13]  G. Temple,et al.  GENERALIZED FUNCTIONS, VOL. I , 1965 .

[14]  Philip E. Sarachik.  Controllability and observability of linear systems , 1997 .

[15]  W. Rheinboldt,et al.  Time-Dependent, Linear DAE's with Discontinuous Inputs , 1994 .

[16]  Werner C. Rheinboldt,et al.  CLASSICAL AND GENERALIZED SOLUTIONS OF TIME-DEPENDENT LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS , 1996 .