Computing the regularization of a linear differential-algebraic system

Abstract We study the regularization problem for linear differential–algebraic systems. As an improvement of former results we show that any system can be regularized by a combination of state-space and input-space transformations, behavioral equivalence transformations and a reorganization of variables. The additional state feedback which is needed in earlier publications is shown to be superfluous. We provide an algorithmic procedure for the construction of the regularization and discuss computational aspects.

[1]  Ricardo Riaza,et al.  Differential-Algebraic Systems: Analytical Aspects and Circuit Applications , 2008 .

[2]  Volker Mehrmann,et al.  Regularization of linear and nonlinear descriptor systems , 2011 .

[3]  P. Dooren,et al.  An improved algorithm for the computation of Kronecker's canonical form of a singular pencil , 1988 .

[4]  Timo Reis,et al.  Regularization of linear time-invariant differential-algebraic systems , 2015, Syst. Control. Lett..

[5]  P. Van Dooren,et al.  A pencil approach for embedding a polynomial matrix into a unimodular matrix , 1988 .

[6]  T. Berger,et al.  Hamburger Beiträge zur Angewandten Mathematik Controllability of linear differential-algebraic systems-A survey , 2012 .

[7]  I. Higueras,et al.  DIFFERENTIAL-ALGEBRAIC SYSTEMS: ANALYTICAL ASPECTS AND CIRCUIT APPLICATIONS , 2009 .

[8]  René Lamour,et al.  Differential-Algebraic Equations: A Projector Based Analysis , 2013 .

[9]  J. Willems.  The Behavioral Approach to Open and Interconnected Systems , 2007, IEEE Control Systems.

[10]  T. Berger.  On differential-algebraic control systems , 2013 .

[11]  Gene H. Golub,et al.  Matrix computations , 1983 .

[12]  Peter Benner,et al.  Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations , 2015 .

[13]  Jan C. Willems,et al.  Introduction to mathematical systems theory: a behavioral approach, Texts in Applied Mathematics 26 , 1999 .

[14]  M. A. Akanbi,et al.  Numerical solution of initial value problems in differential - algebraic equations , 2005 .

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

[16]  Frank M. Callier.  Book review: J. W. Polderman and J.C. Willems, "Introduction to Mathematical Systems Theory: a Behavioral Approach" (Springer Verlag 1998) , 2002 .

[17]  T. Berger,et al.  The quasi-Weierstraß form for regular matrix pencils , 2012 .

[18]  Volker Mehrmann,et al.  Differential-Algebraic Equations: Analysis and Numerical Solution , 2006 .

[19]  J. Willems.  Paradigms and puzzles in the theory of dynamical systems , 1991 .