A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for ...

The distributed fusion filtering problem is studied for multi-rate sampling stochastic singular linear systems with multiple sensors and stochastic multiplicative noises. The system is described at the highest sampling rate and different sensors may have different lower sampling rates. The white noise in measurement matrix is introduced to describe the stochastic disturbance. Firstly, based on ...

The geometric approach is a mathematical concept developed to improve the analysis and synthesis of linear multivariable systems. In this article we summarized the foundations for the geometric approach to both linear and singular systems. A mathematical introduction to the controlled and conditioned invariant subspaces has been presented. Additional characteristic subspaces were introduced, su...

In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system |L| of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after suitable twists by powers of L. Moreover we show that similar results hold for subvarieties of a complex abelian variety.

the grace mission has provided scientific community time-variable gravity field solutions with high precision and on a global scale. the grace mission was launched on march 2003. this mission consists of two satellites that pursue each other in their orbit. distance between two satellites in orbit is measured continuously to an accuracy of better than 1 micron using kbr system placed in satelli...

We study a useful numerical invariant of normal surface singularities, introduced recently by T. Kawachi. Using this invariant, we give a quick proof of the (well-known) fact that all log-canonical surface singularities are either elliptic Gorenstein or rational (without assuming a priori that they are Q -Gorenstein). In §2 we prove effective results (stated in terms of Kawachi’s invariant) reg...

In this paper, an x n fully fuzzy linear system à ⊗ x = b where à is a fuzzy matrixx and b are fuzzy vectors with trapezoidal fuzzy numbers is solved by singular value decomposition method. The method is illustrated with numerical examples.

This paper concerned with a model reduction of infinite dimensional systems by using the singular perturbation approximation. The system considered is that of the exponentially stable linear system with bounded and finite-rank input and output operators such that the balanced realization can be performed on the system. Furthermore, the singular perturbation method is applied to reduce the order...

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided. Keywords—Matrix equation, Generalized inverse, Generalized singular-value decomposition.

Characterization of singular graphs can be reduced to the non-trivial solutions of a system of linear homogeneous equations Ax = 0 for the 0-1 adjacency matrix A. A graph G is singular of nullity η(G) ≥ 1, if the dimension of the nullspace ker(A) of its adjacency matrix A is η(G). Necessary and sufficient conditions are determined for a graph to be singular in terms of admissible induced subgra...