Positive realization of difference equations
- 1 January 1981
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuits and Systems
- Vol. 28 (1) , 39-47
- https://doi.org/10.1109/tcs.1981.1084906
Abstract
The problem treated here is that of realization of an nthorder linear difference equationd(D)y = 0describing free responses of a physical system in the formx(k + 1)=Ax(k), y(k)=c'x(k), where the elements of matrix A and vector c are restricted to be nonnegative to reflect physical constraints. The specific problem treated here are realizability conditions, and characterizations of minimal realizations. These problems are discussed in detail through a geometric approach, specifically through the convex analysis. It is shown that the necessary and sufficient condition for realizability and the minimal dimension are completely characterized by a convex cone derived from the difference equation. A matrix equation generating all possible realizations is obtained, and then the canonical structure of minimal realizations is derived.Keywords
This publication has 3 references indexed in Scilit:
- Charge-routing networksIEEE Transactions on Circuits and Systems, 1979
- Compartmental system analysis: Realization of a class of linear systems with physical constraintsIEEE Transactions on Circuits and Systems, 1977
- Linear Multivariable SystemsPublished by Springer Nature ,1974