Discretising effectively a linear singular differential system by choosing an appropriate sampling period

Two main goals are to discretise the solution of an autonomous linear singular continuous-time system and to compare the discretised with the continuous solution at fixed time moments. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena. The complex Kronecker canonical form decomposes the singular system into five sub-systems, whose solutions are obtained. Moreover, in order for the norm of the difference between the two solutions to be smaller than a fully pre-defined, acceptable bound, the sampling period should be arranged in a particular interval. A numerical example is also available.

[1]  Thomas Kailath,et al.  Generalized dynamical systems , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[2]  S. Campbell.  Singular linear systems of differential equations with delays , 1980 .

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

[4]  V. Mehrmann.  The Autonomous Linear Quadratic Control Problem , 1991 .

[5]  David A. Kendrick,et al.  On the Leontief Dynamic Inverse , 1972 .

[6]  Basil G. Mertzios,et al.  On Kalman's controllability and observability criteria for singular systems , 1999 .

[7]  Wassily Leontief.  Input-Output Economics , 1966 .

[8]  G. Verghese.  Infinite-frequency behaviour in generalized dynamical systems , 1978 .

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

[10]  S. Campbell.  Singular Systems of Differential Equations , 1980 .

[11]  G. Hayton,et al.  Generalised Autonomous Dynamical Systems, Algebraic Duality and Geometric Theory , 1981 .

[12]  Nicholas P. Karampetakis,et al.  On the discretization of singular systems , 2004, IMA J. Math. Control. Inf..

[13]  Jr. G. Forney,et al.  Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems , 1975 .

[14]  V. Mehrmann.  The Autonomous Linear Quadratic Control Problem: Theory and Numerical Solution , 1991 .

[15]  A. Rachid.  A remark on the discretization of singular systems , 1995, Autom..

[16]  F. Lewis.  A survey of linear singular systems , 1986 .

[17]  D. Luenberger,et al.  SINGULAR DYNAMIC LEONTIEF SYSTEMS1 , 1977 .

[18]  N. Karcanias.  Matrix pencil approach to geometric system theory , 1979 .

[19]  H. Neudecker,et al.  Kendrick's “Forward Integration Method” and the Dynamic Leontief Multisectoral Model , 1976 .

[20]  P. Dooren.  Reducing subspaces: Definitions, properties and algorithms , 1983 .

[21]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.

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

[23]  D. A. Livesey,et al.  The singularity problem in the dynamic input-output model† , 1973 .