Model reduction by moment matching for linear time-invariant (LTI) models is a technique that has clear interpretation in the Laplace domain. In particular, multiple-input multiple-output (MIMO) LTI case, Krylov subspace methods aim at transfer-function matrix (and possibly its derivatives) of reduced-order model to full-order along so-called tangential directions desired interpolation points. ...

This article provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations notions are studied general dynamics, and associated Lyapunov inequalities derived. The system dynamics may depend on any type process in our framework. Our results the can immediately lead us to more specific tractable conditions when underlying is restr...

The sum of the first n ≥ 1 eigenvalues of the Laplacian is shown to be maximal among triangles for the equilateral triangle, maximal among parallelograms for the square, and maximal among ellipses for the disk, provided the ratio (area)/(moment of inertia) for the domain is fixed. This result holds for both Dirichlet and Neumann eigenvalues, and similar conclusions are derived for Robin boundar...

A fast computation technique is proposed in this paper to speed up the process of model order reduction for parameterized systems. The key step and also the main computational load of many model order reduction methods is the computation of a projection matrix V which requires computing moment matrices of the systems. For computing each moment matrix, the solution of a linear system with multip...