Minimal representations of implicit linear systems
The paper investigates a generalized linear system description with the purpose i) to establish a set of simple conditions necessary and sufficient for the linear system model to be minimal in a certain well- defined sense, and ii) to set up a stable algorithm for deriving a minimal representation from a non-minimal one. The conditions for minimality are formulated in four properties concerning row- as well as column regularities of matrices which form the partitioned coefficient matrix of the associated homogeneous linear system. So, four rank tests are needed to check minimality. Two of them correspond to generalizations of controllability and observability criteria, the third one corresponds to removal of system poles at infinity, and the last one takes into account the set of algebraically dependent variables. For linear state-space models two of the four criteria are always valid. The four steps in the minimization algorithm correspond to the four properties necessary for minimality. A pseudo- algorithmic language is used for description of the procedures. They are tested in an illustrative numerical example.
scientific article; zbMATH DE number 3902476
scientific article