Generic Controllability Research Articles

Algorithms to verify generic causality and controllability of descriptor systems

Graph-theoretic algorithms are developed for determining generic causality and controllability of structured descriptor systems (SDS's). For the case of nonsingular <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> , a completely graph-theoretic characterization of generic controllability of SDS's is developed. The case of singular <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> is partially resolved, with graph-theoretic characterization of necessary conditions and sufficient conditions for generic causality and controllability developed separately. Although not stated explicitly, these results can be easily translated into a graph-theoretic algorithm to test for generic observability of SDS's.

Generic controllability theorems for descriptor systems

This paper presents an extension of the structural controllability theorem to the case of structured descriptor systems (SDS). A major difficulty in this problem is the loss of independence among the entries of the system matrices. This difficulty is resolved by introducing the idea of column structured matrices (CSM). First, the paper defines and characterizes C - and R -controllability for descriptor systems. Then, the generic controllability theorem is proved, extending the structural controllability theorem to column structured systems (CSS). Finally, based on this result, necessary conditions and sufficient conditions for generic R - and C -controllability are obtained. The result gives a complete characterization of generic controllability for SDS with nonsingular E , and a partial solution for the case of singular E .

Generic properties of column-structured matrices

A matrix is said to be a structured matrix (SM) if its entries are either fixed zeros or mutually independent free parameters. Several generic properties concerning the eigenvalues and eigenvectors of such a matrix are known. Very little is known, however, about the case where the entries of matrices are independent. If, for example, A, B, C, and D are mutually independent SMs (of dimension n× n), then AB, A −1, and ABC+ CD are not SMs in general, since the entries of these matrices are usually interrelated. However, the entries in these matrices are columnwise independent; that is, all elements in an arbitrary column can be simultaneously multiplied by an arbitrary scalar, without affecting other columns, and the result is still a matrix of the same class. A matrix with this property is referred to as a column-structured matrix (CSM). We investigate generic properties of CSMs, and establish nonrepeatedness, nonzeroness, and controllability of the nonzero eigenvalues and eigenvectors of such a matrix. These results have an important application to the problem of generic controllability of structured descriptor systems.

Non-interacting control of macroeconomic variables: Implications on policy mix condiderations

In this paper we study the dynamic path controllability of discrete-time nonlinear economic models in state-space form. First we present an algorithmic procedure for testing this property for time-varying linear systems. Secondly we extend this method to general nonlinear models and we show that under generic conditions path controllability around a specific trajectory of the nonlinear system is equivalent to path controllability of the corresponding linearized model. The results are illustrated with two economic examples.