Descriptor variable systems consist of a mixture of static and dynamic equations. This paper investigates the structural characteristics of linear time-invariant descriptor systems and develops an efficient technique for converting a descriptor system to recursive form, if such a conversion is possible. The paper exploits the connection between descriptor systems and the classical theory of matrix pencils. This yields a canonical form for descriptor systems. The main contribution of the paper is the shuffle algorithm. This algorithm serves both as a test for the solvability of a descriptor system, and as a procedure for converting a system to recursive form, without a change of variable.
[1]
D. Luenberger.
Dynamic equations in descriptor form
,
1977
.
[2]
H. W. Turnbull,et al.
An Introduction to the Theory of Canonical Matrices
,
1932,
Nature.
[3]
H. Rosenbrock,et al.
State-space and multivariable theory,
,
1970
.
[4]
Stephen L. Campbell,et al.
Applications of the Drazin Inverse to Linear Systems of Differential Equations with Singular Constant Coefficients
,
1976
.
[5]
David Jordan,et al.
On state equation descriptions of linear differential systems
,
1975,
1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.