To solve a stochastic linear evolution equation numerically, nite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This appro...

We establish a Sturmian type theorem comparing the number of focal points of any conjoined basis of a nonoscillatory linear Hamiltonian differential system with the number of focal points of the principal solution. We also present various extensions of this statement.

Some new approximation methods are proposed for the numerical evaluation of the finitepart singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several s...

Consider the linear system of equations Bx = f, where B is an N x N singular matrix, but the system is consistent. In this work we show that iterative techniques coupled with vector extrapolation methods can be used to obtain (approximations to) a solution of Bx = f. We do this by extending the results of some previous work on vector extrapolation methods as they apply to nonsingular matrices B...

The problem of input–output decoupling by state feedback is considered for linear time-varying singular systems. Assumptions are introduced, and an algorithm is developed such that the system can be expressed in a simple normal form. A time-varying feedback law is then constructed which ensures, under appropriate conditions, that the closed-loop system is regular, impulse-free, and noninteractive.

This paper undertakes the synthesis of a logic-based switching H2/H∞ state-feedback controller for continuous-time LTI singular perturbation systems. Our solution achieves a minimum bound on the H2 performance level, while also satisfying the H∞ performance requirements. The proposed hybrid control scheme is based on a fuzzy supervisor managing the combination of two controllers. A convex LMI-B...

Controllability and observability of analytically solvable linear time-varying singular systems are considered. Our analysis includes the possible impulsive zero-input response. Based on the definitions of controllability and observability naturally extended from the ones adopted in the time-invariant setting, sufficient and necessary conditions for these two properties are derived. Furthermore...

The PageRank algorithm is used today within web information retrieval to provide a content-neutral ranking metric over web pages. It employs power method iterations to solve for the steady-state vector of a DTMC. The defining one-step probability transition matrix of this DTMC is derived from the hyperlink structure of the web and a model of web surfing behaviour which accounts for user bookmar...

This paper considers linear time-invariant decentralized singular systems which are either nonregular or, if they are regular, they have impulsive modes. It derives algebraic necessary and sufficient conditions for making a singular system both regular and impulsefree by decentralized output feedback control laws and decentralized proportional-plus-derivative output feedback control laws.

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...