In this paper, the problem of reducing a given LTI system into a left or right invertible one is addressed and solved with the standard tools of the geometric control theory. First, it will be shown how an LTI system can be turned into a left invertible system, thus preserving key system properties like stabilizability, phase minimality, right invertibility, relative degree and infinite zero st...

In this paper we address the invertibility of invisible watermarking schemes for resolving rightful ownerships, and present attacks which can cause confusion to rightful claims. We shall show that non-invertibility is a necessary but not sufficient condition in resolving ownership disputes. We then define quasi-invertible watermarking schemes, and, present analysis that links invertibility and ...

In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of fiel...

In this paper we consider a class of Discrete-Event Dynamic Systems (DEDS) modeled as finite-state automata in which only some of the transition events are directly observed. An invertible DEDS is one for which it is possible to reconstruct the entire event string from the observation of the output string. The dynamics of invertibility are somewhat complex, as ambiguities in unobservable events...

The paper deals with the generalized Drazin invertibility of combinations of idempotents p, q in a Banach algebra. It proves the equivalence of the generalized Drazin invertibility of p−q and p+q, as well as the equivalence of the generalized Drazin invertibility of the commutator pq − qp and anticommutator pq + qp of p, q. It extends several results of J. Math. Anal. Appl. 359 (2009) 731–738, ...

We review the concepts of local and global invertibility for a nonlinear auto-regressive moving-average (NLARMA) model. Under very general conditions, a local invertibility analysis of a NLARMA model admits the generic dichotomy that the innovation reconstruction errors either diminish geometrically fast or grow geometrically fast. We derive a simple sufficient condition for a NLARMA model to b...