Singular systems have been studied extensively during the last two decades due Abstract to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associa...

The paper solves a long standing problem of finding error bounds for a general perturbation of the Drazin inverse. The bounds are given in terms of the distance between the matrices together with the distance between their eigenprojections. Estimates using the gap between subspaces are also given. Recent results of several authors, including Castro, Koliha, Straškraba, Wang and Wei can be recov...

In this paper, we extend Jacobson's lemma for Drazin inverses to the generalized \(n\)-strong in a ring, and prove that \(1-ac\) is invertible if only \(1-ba\) invertible, provided \(a(ba)^{2}=abaca=acaba=(ac)^{2}a\). addition, left right Fredholm operators, furthermore, consistent invertibility spectral property index are investigated.

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder’s theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of σ(T ). As applications, we show that if T is algebraically M -hyponormal, or if T is algebraically paranormal, then the generalized Weyl’s theore...

some necessary and sufficient conditions are given for the existence of a g-positive (g-repositive) solution to adjointable operator equations $ax=c,axa^{left( astright) }=c$ and $axb=c$ over hilbert $c^{ast}$-modules, respectively. moreover, the expressions of these general g-positive (g-repositive) solutions are also derived. some of the findings of this paper extend some known results in the...

In this paper, let A and B be n x p complex tensors = + E. Denote the T-Drazin inverse of by AD. We give a perturbation bound for ||BD-AD||=||AD|| under condition (W). Considering solution singular tensor equation A* b, (b ? R(AD)) at same time. The optimal system equations have been given.