Working with a general class of linear Hamiltonian systems on intervals at least one singular endpoint which can be limit-point, limit-circle, or limit-intermediate, we show that renormalized oscillation results obtained in natural way through consideration the Maslov index associated appropriately chosen paths Lagrangian subspaces C2n. In first part analysis associate our families well-defined...

The present paper considers singular value decomposition (SVD) for a class of linear time-varying systems. The class considered herein describes timedriven switched linear systems. Based on an appropriate input-output description, the calculation method of singular values and singular vectors is derived. The SVD enables us to characterize the dominant input–output signals using singular vectors...

Abstract: Reduction of singular fractional systems to standard fractional systems and decomposition of singular fractional discrete-time linear systems into dynamic and static parts are addressed. It is shown that if the pencil of singular fractional linear discrete-time system is regular then the singular system can be reduced to standard one and it can be decomposed into dynamic and static pa...

Keywords: Additive/multiplicative splitting iteration method Singular linear systems Hermitian matrix Semiconvergence a b s t r a c t In this paper, we investigate the additive, multiplicative and general splitting iteration methods for solving singular linear systems. When the coefficient matrix is Hermitian, the semiconvergence conditions are proposed, which generalize some results of Bai [Z....

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

There is much literature about the study of the consensus problem in the case where the dynamics of the agents are linear systems, but the problem is still open for the case where the dynamic of the agents are singular linear systems. In this paper the consensus problem for singular multi-agent systems is considered, in which all agents have an identical linear dynamic mode that can be of any o...